Consider the sequence 2/4, 3/5, 4/6, 5/7,... Which statement describes the sequence?

The sequence diverges.

The sequence converges to 0.

The sequence converges to 1.

The sequence converges to [infinity].

Answers

Answer 1

Answer:

The sequence converges to 1.

Step-by-step explanation:

Sequence 2/4, 3/5, 4/6, 5/7

This sequence can be summarized as:

[tex]\sum_{n=0}^{\infty} \frac{n+2}{n+4}[/tex]

To test if it converges, we can calculate the limite of [tex]\frac{n+2}{n+4}[/tex] as n goes to infinite.

Limit:

[tex]\lim_{n \rightarrow \infty} \frac{n+2}{n+4}[/tex]

Considering only the terms with the highest exponent in the numerator and the denominator:

[tex]\lim_{n \rightarrow \infty} \frac{n+2}{n+4} = \lim_{n \rightarrow \infty} \frac{n}{n} = \lim_{n \rightarrow \infty} 1 = 1[/tex]

Thus, the sequences converges to 1.


Related Questions

What is the following values of:

XZ:

XY:

Answers

it’s 5 square root 2 and 5

Work out the sum of 1/4 1/6 and 1/3

Answers

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

[tex]\frac{1}{4} +\frac{1}{6} +\frac{1}{3}[/tex]

4 = 2 × 2 × 1

6 = 2 × 3 × 1

3 = 3 × 1

GCF = 1

4 × 6 × 3 = 72

[tex]\frac{18}{72} +\frac{12}{72} +\frac{24}{72}[/tex]

[tex]\frac{18+12+24}{72}[/tex]

[tex]\frac{54}{72}[/tex]

54 = 2 × 3 × 3 × 3

72 = 2 × 2 × 2 × 3 × 3

GCF = 2 × 3 × 3

GCF = 18

[tex]\frac{\frac{54}{18} }{\frac{72}{18} }=\frac{3}{4}[/tex]

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\textsf{Looking for your LCD (Least Common Denominator) of each fraction}\downarrow\\\\\\\mathsf{\dfrac{1}{4}=\dfrac{3}{12}}\\\\\\\mathsf{\dfrac{1}{6}=\dfrac{2}{12}}\\\\\\\mathsf{\dfrac{1}{3}=\dfrac{4}{12}}\\\\\\\\\\\large\textsf{The LCD is \underline{12}}[/tex]

[tex]\mathsf{\dfrac{1}{4}+\dfrac{1}{6}+\dfrac{1}{3}}[/tex]

[tex]\mathsf{= \ \dfrac{1\times3}{4\times3}+\dfrac{1\times2}{6\times2}+\dfrac{1\times4}{3\times4}}[/tex]

[tex]\large\textsf{Solving for the numerators (TOP numbers)}\downarrow\\\\\mathsf{1\times3=\boxed{\bf 3}}\\\\\mathsf{1\times2=\boxed{\bf 2}}\\\\\mathsf{1\times4=\boxed{\bf 4}}[/tex]

[tex]\large\textsf{Solving for the denominators (BOTTOM numbers)}\downarrow\\\\\mathsf{4\times3=\boxed{\bf 12}}\\\\\mathsf{6\times2=\boxed{\bf 12}}\\\\\mathsf{3\times4=\boxed{\bf 12}}[/tex]

[tex]\mathsf{=\ \dfrac{3+2+4}{12}}[/tex]

[tex]\large\textsf{Solving for your numerator (TOP number) }\downarrow\\\\\\\mathsf{3+2+4}\\\\\mathsf{= 5+4}\\\\\mathsf{= \boxed{\large\textsf{\bf 9}}}[/tex]

[tex]\mathsf{=\ \dfrac{9}{12}}[/tex]

[tex]\mathsf{\dfrac{9\div3}{12\div3}}\\\\\\\\\mathsf{9\div3= \boxed{\large\textsf{\bf 3}}}\\\\\mathsf{12\div3=\boxed{\large\textsf{\bf 4}}}[/tex]

[tex]\mathsf{= \dfrac{3}{4}}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: }\boxed{\mathsf{\bold{ \dfrac{9}{12}\ or\ \dfrac{3}{4}}\ either\ of\ those\ fractions\ should\ work\ because}}}}\\\boxed{\boxed{\large\textsf{they are equal to each other!}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Need help with this

Answers

Answer 26 explanation 9+9+4+4=26

If f(x) = 3x - 1 and g(x) = x + 2, find (f- g)(x).
PLZZ HELPPP

Answers

This the answer

If f(x) = 3x - 1 and g(x) = x + 2, find (f- g)(x).

PLZZ HELPPP

2x-3

Find an equation in point-slope form for the line having the slope m =1/3 and containing the point (-3,- 6).

Answers

The answer is: y + 6= 1/3 (x + 3)

The measures of the exterior angles of a hexagon are x°, 2x°, 4x°, 6x°, 7x°, and 10x°. Find the measure of the smallest exterior angle.

Answers

Answer

x is the smallest angle so 12 is the answer.

Step-by-step explanation:

x + 2x + 4x + 6x + 7x + 10x = 360 degree (sum of exterior angles of a hexagon)

30x = 360

x = 360/30

x = 12

the smallest exterior angle of hexagon is 12 degree.

The measure of the smallest exterior angle is 12 degrees.

What is Polygon?

Polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

A hexagon is a six-sided polygon or 6-gon creating the outline of a cube.

The measures of the exterior angles of a hexagon are x°, 2x°, 4x°, 6x°, 7x°, and 10x°.

We need to find the smallest exterior angle which is x.

we know that the sum of the exterior angles of any polygon is always equal to 360.

x° + 2x° + 4x° + 6x° + 7x° + 10x° = 360

30x=360

Divide both sides by 30

x=360/30

x=12

Hence, the measure of the smallest exterior angle is 12 degrees.

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To learn more on Polygons click:

https://brainly.com/question/28276384

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Ryan draws a trend line through the following data
points. Did he draw the line correctly?

Answers

Answer: C, You can tell the trend line is incorrect since all of the points are below it. A trend line should be in-between all of the points to give the best estimate.

Step-by-step explanation:

How can -6/4x = 12 be solved in one step?​

Answers

Answer:

Multiply each side by -4/6 to isolate x

Step-by-step explanation:

-6/4x = 12

Multiply each side by -4/6 to isolate x

-4/6 *(-6/4x) = 12*(-4/6)

x =-8

Answer:

12 divided by -6/4

Step-by-step explanation:

you need to isolate the x, since -6/4 is being multiplied to x, you gotta divide it to move -6/4 to the other side x=12 divided by -6/4

math:John is buying new shoes. He finds the shoes he wants on sale for 30%, and the original price is $88. How much will he pay for the shoes?

Answers

Answer:

26.4

Step-by-step explanation:

hd hd hd hd hd hd hd hd hd hd hd hd

Answer:$61.6

Step-by-step explanation: The sale is 30% so we have to look for 70% of $88 because that's what we're paying for. So, that would be 88 times 70/100 which ends with 61.6.

x³+y³=(x+y)(x² - xy +y²)​

Answers

Answer:

__________________________________

➡️x3+y3 = (x+y)(x^2-xy+y^2)

--------------------

R.H.S

(x+y)(x^2-xy+y2)

=>x3-x^2y+xy^2+x^2y-y^2x+y3

NOW after cancelling we get :

=> x3+y3

-------------------

L.H.S

=> x3+y3

L.H.S. = R.H.S

Hence VERIFIED✔✔

_______________________________

Step-by-step explanation:

A can of soup is 8 centimeters in diameter and 10 centimeters high. What is the volume of the can in terms of ?

Answers

Answer:

volume= 502.4cm

Step-by-step explanation:

see attachment for detailed solution

Answer:

Step-by-step explanation:

Formulae for Volume = Pi x r2 x h

Pi = 3.14 or 314/100 because the radius is not a product of 7

Radius = 4 cm

Height = 10 cm

314/100 x 4 x 4 x 10 = 512.4 cm2

= 512.4 cm2

The sum of three numbers is 86. The third number is 4 times the first. The first number is 10 more than the second. What are the numbers?

Answers

Answer:

The first number is 16

The second number is 6

The third number is 64

Step-by-step explanation:

The information from the word problem are;

The count of the numbers in the sum = 3 numbers

The value of the sum of the three numbers = 86

The value of the third number = 4 × The value of the first number

The value of the first number = 10 + The value of the second

Let 'x' represent the first number, let 'y' represent the second number and let 'z' represent the third number, we have;

x + y + z = 86...(1)

z = 4 × x...(2)

x = y + 10...(3)

From equation (3), we get;

x = y + 10

∴ y = x - 10...(4)

Substituting the value of z from equation (2) and the value of y from equation (4) in equation (1) gives;

x + y + z = 86

z = 4 × x = 4·x

y = x - 10

∴ x + y + z = x + (x - 10) + 4·x = 86

x + (x - 10) + 4·x = x + x - 10 + 4·x = 6·x - 10 = 86

6·x = 86 + 10 = 96

∴ x = 96/6 = 16

x = 16

From equation (2), we get;

z = 4 × x

∴ z = 4 × 16 = 64

z = 64

From equation (4), we get

y = x - 10

∴ y = 16 - 10 = 6

y = 6

Therefore; x = 16, y = 6, and z = 64

The numbers are 16, 6, and 64

Is anyone free to help me? It's a picture .

Answers

Answer:

1. 8 units downwards and 2 units left

2.7 units right and 4 units upwards

3. 5 units right and 4 units downwards

Step-by-step explanation:

That how it goes

Please fill the blanks

Answers

Answer:

First box

8pi-(7pi/4)= pi/4

Second Box:

Tan 7pi/4= 0.09625006863

Step-by-step explanation:


Find the sum of the series
{1875 + 750 + 300+...
+3.072}

Answers

Answer:

Find the indicated sum for each geometric series.

{1875+750+300+⋯+3.072}

Answer: 3122.952

Step-by-step explanation:

{1875+750+300+⋯+3.072}

r=0.4 3.072=1875(0.4)n−1

0.0016384=(0.4)n−1

7=n−1→n=8

Sn=1875(1−(0.4)8)1−0.4=3122.952

I think is like this.

For the following system, use the second equation to make a substitution for x in the first equation.

3x + 2y = 7
x - y + 3 = 0

What is the resulting equation?

Answers

Step-by-step explanation:

x value is 0.2

y value is 3.2

Un microempresario realiza una inversión donde le pagan una rentabilidad del 5,36% mensual simple, él desea que esa inversión se triplique ¿Cuánto tiempo deberá esperar para que esto ocurra?

Answers

Answer:

Deberá esperar 37.31 años para que esto ocurra.

Step-by-step explanation:

Este es un problema de interés simple.

La fórmula del interés simple viene dada por:

[tex]E = P*I*t[/tex]

En el que E es la cantidad de interés ganado, P es el principal (la cantidad inicial de dinero), I es la tasa de interés (anual, como decimal) y t es el tiempo.

Después de t años, la cantidad total de dinero es:

[tex]T = E + P[/tex]

5,36% mensual simple

Esto implica que [tex]I = 0.0536[/tex]

Inversión se triplique ¿Cuánto tiempo deberá esperar para que esto ocurra?

Tiempo t para que la cantidad de interés sea lo doble de la cantidad inicial, o sea, [tex]E = 2P[/tex].

[tex]E = P*I*t[/tex]

[tex]2P = P*I*t[/tex]

[tex]It = 2[/tex]

[tex]0.0536t = 2[/tex]

[tex]t = \frac{2}{0.0536}[/tex]

[tex]t = 37.31[/tex]

Deberá esperar 37.31 años para que esto ocurra.

Which of the following is the maximum value of the function y = −2x2 + 5?


5


−2


25


0

Answers

i think its 5 not sure tho

Answer:

The answer is 0 because the minimum is 5

Step-by-step explanation:

Use the formula  

x  =  −  b /2 a

to find the maximum and minimum.

( 0 , 5 )

How many mLs are in 1300mG

Answers

Answer:

1.3 mL

Step-by-step explanation:

1 mg = 0.001 mL

1300 mg * 0.001 mL/mg = 1.3 mL

first answer is Correct here is way they are correct 1300 Milligram (mg) 1.300000 Milliliters (ml)
1 mg = 0.001000 ml 1 ml = 1,000 mg so 1.3 is the correct answer How many Milliliters in 1300 Milligram?
The answer is 1.300000

An apartment has 90 square meters of carpeting. How much is this in square feet? Use the following conversion: 1 square meter is 10.8 square feet.

An explanation on how to do it would also be amazing!

Answers

Answer:

Area = 972 square feet

Step-by-step explanation:

Let  90 square meter be = x square feet

Given :

                      square meter             square feet

                              1                             10.8

                             90                            x

[tex]\frac{1}{90} = \frac{10.8}{x}\\\\1 \times x =10.8 \times 90 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ cross \ multiply \ ]\\\\x = 972[/tex]

Therefore , 90 square meter = 972 square feet

Given d= 4t+1 can you determine the value of the y-
intercept?

HELP!! asap!

Answers

Yes. The y-intercept is 1 since the equation for a line is equal to y=mx+b, where b is the y-intercept.

verify that :- 2/7 x (-3/5 +4/10)=2/7x-3/5 +2/7 x 4/10
please help me fast please​

Answers

Answer:

hope it helps you............

Answer:

-2/35.....................

please help!!! i’ll give brainliest.

no links
do not comment random things
i need asap!!
ill give as many points as i can

Answers

Answer:

a,d,e

Step-by-step explanation:

75+a1 = 180

so a1=105

a1=x-15

105=x-15

x=120

then using rules of parallel lines with commone intersecting line gives the others.

find the product write your question in exponential form 7 ^-1 x 7 ^-7

Answers

Answer:

[tex] {7}^{ - 8} [/tex]

Step-by-step explanation:

[tex] {7}^{ - 1} \times {7}^{ - 7} \\ {7}^{ - 1 + - 7} \\ {7}^{ - 8} [/tex]

Hope this helps you.

Select the correct answer.
What is the solution for x in the equation?
-x + 3/7 = 2x - 25/7

Answers

Answer:

= 4/ 3

Step-by-step explanation:

-x+3/7=2x-25/7

We move all terms to the left:

-x+3/7-(2x-25/7)=0

We add all the numbers together, and all the variables

-x-(+2x-25/7)+3/7=0

We add all the numbers together, and all the variables

-1x-(+2x-25/7)+3/7=0

We get rid of parentheses

-1x-2x+25/7+3/7=0

We multiply all the terms by the denominator

-1x*7-2x*7+25+3=0

We add all the numbers together, and all the variables

-1x*7-2x*7+28=0

Wy multiply elements

-7x-14x+28=0

We add all the numbers together, and all the variables

-21x+28=0

We move all terms containing x to the left, all other terms to the right

-21x=-28

x=-28/-21

x=1+1/3

Answer:

x = [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

Given

- x + [tex]\frac{3}{7}[/tex] = 2x - [tex]\frac{25}{7}[/tex] ( multiply through by 7 to clear the fractions )

- 7x + 3 = 14x - 25 ( subtract 14x from both sides )

- 21x + 3 = - 25 ( subtract 3 from both sides )

- 21x = - 28 ( divide both sides by - 21 )

x = [tex]\frac{-28}{-21}[/tex] = [tex]\frac{4}{3}[/tex]

PLZZ HELPPPPPP!!!!!!!!

Answers

Answer:

$1043.33  

$494.47(1 +1)(1 + .055)

Step-by-step explanation:

A regular decagon has a radius of 8 cm.

What is the approximate area of the decagon? Recall that a decagon is a polygon with 10 sides.

188 cm2
198 cm2
304 cm2
375 cm2

Answers

Answer:

188cm^2

Step-by-step explanation:

A regular decagon has ten sides. Therefore, a decagon with radius of 8 cm has an approximate area of 188 cm²

What is a decagon?

A decagon is a polygon with 10 sides.

Therefore, the approximate area of a decagon can be found as follows:

area of decagon =  r²sin(360/n) / 2 × 10

where

r = radius

n = number of sides

Therefore,

r = 8 cm

area of decagon = 8² sin (360/ 10) / 2 (10)

area of decagon = 64 sin 36 / 2 × 10

area of decagon = 64 × 0.58778525229 / 2 × 10

area of decagon = 37.6182561467 / 2 × 10

area of decagon = 18.8091280734 × 10

area of decagon = 188 cm²

learn more on decagon here: https://brainly.com/question/27314677

helppppppppppppppppp

Answers

Answer:

Click the third one.

Answer:

3rd one

Step-by-step explanation:

Mark me brainliest pls

Hope this helps!

what fraction of 3 hours is 30 minutes?​

Answers

Answer:

7/2

Step-by-step explanation:

I need help with this! Quick ASAP?

Answers

Answer:

a) F

b) B, E, D

Step-by-step explanation:

a) The segment with the greatest gradient has the largest change in y-values per unit change in x-values

From the given option, the rate of change of the y to the x-values of B = the gradient = (4 units)/(2 units) = 2

The gradient of F = (-3units)/(1 unit) = -3

The gradient of A = 4/4 = 1

The gradient of C = -2/5

The gradient of D = 2/6 = 1/3

The gradient of E = 3/4

The segment with the greatest gradient is F

b) The steepest segment has the higher gradient

From their calculated we have;

The gradient of segment B = 2 therefore, B is steeper than E that has a gradient of 3/4, and E is steeper than D, as the gradient of D = 1/3

Therefore, we have;

B, E, D.

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