How do you do this question?

How Do You Do This Question?

Answers

Answer 1

Answers:

[tex]\displaystyle \lim_{n \to \infty} \frac{a_n}{b_n} = 6[/tex]

Based on the limit comparison test, the series is convergent

========================================================

Explanation:

As n gets really large, the terms [tex]3^n[/tex] and [tex]3^n-2[/tex] are effectively the same. Taking the limit to infinity of the ratio leads to 1.

In other words,

[tex]\displaystyle \lim_{n \to \infty} \frac{3^n}{3^n-2} = \lim_{n \to \infty} \frac{3^n}{3^n} = 1[/tex]

That -2 doesn't really play a role when n gets very large.

This result is then multiplied by the 6 in the [tex]a_n[/tex] sequence, getting 6 as the final limit we want.

So,

[tex]L = \displaystyle \lim_{n \to \infty} \left(a_n \div b_n\right)\\\\\\L = \displaystyle \lim_{n \to \infty} \left(\frac{6}{3^n-2} \div \frac{1}{3^n}\right)\\\\\\L = \displaystyle \lim_{n \to \infty} \left(\frac{6}{3^n-2} \times \frac{3^n}{1}\right)\\\\\\L = \displaystyle \lim_{n \to \infty} \left(\frac{6*3^n}{3^n-2}\right)\\\\\\[/tex]

[tex]L = \displaystyle 6*\lim_{n \to \infty} \left(\frac{3^n}{3^n-2}\right)\\\\\\L = \displaystyle 6*\lim_{n \to \infty} \left(\frac{3^n}{3^n}\right)\\\\\\L = \displaystyle 6*\lim_{n \to \infty} (1)\\\\\\L = \displaystyle 6*1\\\\\\L = \displaystyle 6\\\\\\[/tex]

Since the limiting value is positive and not infinity, this means that both series [tex]\sum a_n[/tex] and [tex]\sum b_n[/tex] converge or they both diverge.

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

If we plug n = 2 into the [tex]b_n[/tex] sequence, we get

[tex]b_n = \frac{1}{3^n}\\\\b_2 = \frac{1}{3^2}\\\\b_2 = \frac{1}{9}[/tex]

The first term is a = 1/9

If we plugged n = 3, we would get [tex]b_3 = \frac{1}{27}[/tex]

This shows that the common ratio is r = 1/3

Because -1 < r < 1 is true, we know that the infinite geometric series converges. Therefore, [tex]\sum b_n[/tex] converges. We don't need to find the converging value.

Going back to the limit comparison test, we stated that both [tex]\sum a_n[/tex] and [tex]\sum b_n[/tex] either diverge together or converge together.

We've shown that the b series converges, so the 'a' series must converge as well.


Related Questions

Darin needs to know the price per pound of clementines. What needs to change in the table so that the data on clementines is in units of pounds and cost?

Answers

Answer:

the table gives the cost for the number of three pounds bag of clemintines we need to change the number of bags to pounds to get the data or clemintines in units of pounds and cost.

Answer:

The table gives the cost for the number of three-pound bags of clementines. We need to change the number of bags to pounds to get the data for the clementines in units of pounds and cost.

Step-by-step explanation:

THIS IS THE SAMPLE ANSWER

5624/6 with a remainder

Answers

Answer:

937.333

Step-by-step explanation:

Answer:

937.33 (rounded. Real answer: 937.333333)

Step-by-step explanation:

5,624 ÷ 6 = 937.33 (rounded since the real answer was: 937.333333)

Please help!
Choose 1 answer:
Monday
Tuesday
Wednesday
Thursday

Answers

Wednesday because Friday is (-4) and you add (-9) it adds too (-13) Wednesday
wednesday is the correct answer

A architect made a scale drawing of a house to be built. The scale is 2 inches to 3 feet. The house in the drawing is 24 inches tall. How tall is the actual house?

Answers

Answer:

36 feet.

Step-by-step explanation:

2 goes into 24 12 times, 12 times 3 is 36 therefore the actual house is 36 feet tall.

Question

5°F - 32)

The function to convert Fahrenheit to Celsius is °C = (°F) =

The inverse function will

9

convert Celsius to Fahrenheit. What is the inverse function? Complete the explanation of how

determining this inverse is different than determining the previous inverses.

The inverse function is °F = -(°C)=

The F and °C (select) V need to be switched like the x and y did in the previous functions.

(select) degree measures, and because of the real-world relationship, switching them

(select) ✓ make sense.

Answers

Answer:

[tex]F = \frac{9C + 32}{5}[/tex]

Step-by-step explanation:

Given

[tex]C = \frac{(5F - 32)}{9}[/tex]

Required

Determine the inverse function

[tex]C = \frac{(5F - 32)}{9}[/tex]

Make F the subject of formula:

Multiply through by 9

[tex]9C = 5F - 32[/tex]

Add 32 to both sides

[tex]9C + 32= 5F[/tex]

Divide through by 5

[tex]\frac{9C + 32}{5}= F[/tex]

[tex]F = \frac{9C + 32}{5}[/tex]

While attending a baseball game, Eva buys hamburgers and hotdogs for her family. The number of hot dogs bought is five more than the number of hamburgers bought. Hamburgers cost $6.25 each and hot dogs cost $3.75 each. Eva spent a total of $58.75 on the hamburgers and hot dogs.

Answers

Answer:

2.35 hamburgers

Step-by-step explanation:

H6.25 + H18.75 = 58.75

a, = 8 + 2(n - 1).

Dose anyone know this.​

Answers

It is 54 because if you add a to 8 you get
the answer is 54 when you add 8 to a :)

∠A and ∠B are supplementary. m∠A = (6x + 12) , m∠B = (x + 28). Find the measure of each angle.

Answers

The answer would be 64

PLEASE HELP ME IM BEGGING YOU!!!
FIND THE VALUE OF X

Answers

84 I'm sure it's that I did it before

x equals 84°, option D (:

one fourth of a number is 12 find the number​

Answers

pretty sure it’s 3. if you multiply .25

Answer:

48

Step-by-step explanation:

If 12 is one-fourth of a number, just multiply 12 by four to find the whole number.

12 x 4 = 48

You could have also set this up as an equation

12 = 1/4x

And then divide 12 by one-fourth

12/(1/4) = 48

Find the value of x
PLEAASEEE HELP!!!

Answers

Answer:

x = 37

Step-by-step explanation:

4x + 3 + x - 8 = 180

4x + x - 8 + 3 = 180

5x - 5 = 180

5x = 185

x = 37

Hope this helps!

I need help !!!!!In the figure shown

Answers

Answer: it is D

Step-by-step explanation:

I WILL MARK BRAINLIEST BUT PLEASE ANSWER FAST

Answers

Answer:

B

Step-by-step explanation:

It had this question on my test. I already answered it. I put c and got it wrong. The answer is B.

SOMEONE HELP WITH MY LAST TWO PROBLEMS

Answers

Answer:

What are your last 2 problems m8

Step-by-step explanation:

Find mo 8 5 m n o
Mo=

Answers

Answer:

MO is 13 units

Step-by-step explanation:

If point lies on a segment, then this point divides the segment into two parts, the sum of their lengths equals the length of the segment

Point N ∈ segment MO

→ That means point N divide segments MO to two parts MN and NO

∴ Point N divides segment MO into two parts MN and NO

→ That mans the length of segment MO equals to the sum of

   lengths of MN and NO

MO = MN + NO

∵ MN = 8 units

∵ NO = 5 units

∴ MO = 8 + 5

MO = 13 units

HELP ME ASAP!!! I WILL MARK BRAINLIEST!!

Answers

I can help
What’s up

Which one is > greater or < less than or = equal to?? 6+√8____√6+8​

Answers

[tex]\huge\boxed{\sqrt{6}+8\;is\;greater\;than \;6+\sqrt{8} }[/tex]

[tex]6+\sqrt[]{8} =8.82\\\sqrt{6}+8=10.44\\\\\boxed{Therefore, \sqrt{6}+8\;is\;greater\;than\;6+\sqrt{8}. }[/tex]

Choose the best explanation that describes in words what the numerical value of the slope tells you.

a. Every increase in coral growth of one centimeter will result in an average of 5.25 fewer degrees Celsius of sea surface temperature per year.
b. Every increase in coral growth of one centimeter will result in an average of 5.25 more degrees Celsius of sea surface temperature per year.
c. Every increase in sea surface temperature of one degree Celsius will result in an average of 0.1578 more centimeters of coral growth per year.
d. Every increase in sea surface temperature of one degree Celsius will result in an average of 0.1578 fewer centimeters of coral growth per year.

Answers

Data for the question :

Sea surface temperature 26.7 26.6 26.6 26.5 26.3 26.1

Growth 0.85 0.85 0.79 0.86 0.89 0.92

Answer:

d. Every increase in sea surface temperature of one degree Celsius will result in an average of 0.1578 fewer centimeters of coral growth per year.

Step-by-step explanation:

Given the data :

Surface Temperature (X) : 26.7 26.6 26.6 26.5 26.3 26.1

Growth (Y) : 0.85 0.85 0.79 0.86 0.89 0.92

Using a regression calculator, we can find the model equation and extract the slope :

The regression equation obtained is :

y=5.039-0.1578x

From y = mx + c

Where m = gradient or slope

c = intercept

x and y are predictor and predicted variables respectively.

Hence, the gradient or slope (m) of the model = - 0.157. We have a negative slope, hence, increase in x will result una decrease in y.

The slope thus means: for every 1 degree increase in sea surface temperature (x), there is an average decline of about 0.1578 cm in growth per year.

Three workers arrive at work 15 minutes late, at a cost of $11 hour.

Answers

Answer:

They earned 8.25

Step-by-step explanation:

If they arrived late 15 minutes, then they lose a 1/4 of the pay. So they'd be making $8.25, and not the full $11 for that first hour.

The correct Standard Form of the equation y=3/2x+3

Answers

Answer:

3x-2y=-6

My mom listening to wap


Write 9/18 as a decimal. Identify the decimal as terminating or repeating.
a. 0.5; repeating
b. 0.9; terminating
c. 0.5; terminating
d. 1; repeating

Answers

Answer:

it is c

Step-by-step explanation:

Answer:

C.) 0.5; Terminating

Step-by-step explanation:

Answer:

918=0.5

Showing the work

You can first reduce this fraction by dividing both the numerator and denominator by the Greatest Common Factor of 9 and 18 using

GCF(9,18) = 9

9÷918÷9=12

We know that

12

is the same as

1÷2

Then using

Long Division for 1 divided by 2

=0.5

Hope I helped

Brainliest plz

all drop down menus are 0-9
use drop down menus to complete each equation so the statement about its solution is true.

Answers

Answer: 5-4+7x+1 = [7]x+[not 2]

5-4+7x+1 = [not 7]x+[any number]

5-4+7x+1 = [7]x+[2]

which postulates make these triangles congruent

Answers

Answer: 1) ASA

2) AAS/SAA

3) Not possible

Step-by-step explanation: 1 is asa because it has 2 angles and a side that are on the same line. 2 is aas/saa because it has a side then two angles. 3 is not possible because it’s ssa and ssa is not used to prove triangles congruent

Find the x-intercept in the function: 3x-2y =6

Answers

Answer:

x=(2,0)

Step-by-step explanation:

3x-2y=6

3x-2(0)=6

3x=6

x=2

Island Water Sports provides rental equipment and instruction for a variety of water sports in a resort town. On one morning, a decision must be made on how many Wildlife Raft Trips and how many Group Sailing Lessons should be scheduled. Each Wildlife Raft Trip requires one captain and one crew person and can accommodate six passengers. The revenue per raft trip is $120. Ten rafts are available, and at least 30 people are on the list for reservations this morning. Each Group Sailing Lesson requires one captain and two crew people for instruction. Two boats are needed for each group. Four students form each group. There are 12 sailboats available, and at least 20 people are on the list for sailing instruction this morning. The revenue per group sailing lesson is $160. The company has 12 captains and 18 crew available this morning. The company would like to maximize the number of customers served while generating at least $1800 in revenue and honoring all reservations. Define the decision variables as follows and formulate the problem as a linear program. Let x be the number of Wildlife raft Trips to be scheduled. Let y be the number of Group Sailing Lessons to be scheduled.
The following constraints complete the problem:
120x + 160y ≥ 1800 (1)
x ≤ 10 (2)
2y ≤ 12 (3)
6x ≥ 30 (4)
4y ≥ 20 (5)
x + y ≤ 12 (6)
x + 2y ≤ 18 (7)
1) What does constraint (1) represent?
A) The maximum number of captions who can be deployed.
B) The maximum number of crews who can be deployed.
C) The minimum revenue requirement.
D) The maximum quantity of the rafts available.
E) The maximum quantity of the sailboats available.
F) The demand of raft trips that must be satisfied.
G) The demand of sailing lessons that must be satisfied.
2) What does constraint (4) represent?
A) The maximum number of captions who can be deployed.
B) The maximum number of crews who can be deployed.
C) The minimum revenue requirement.
D) The maximum quantity of the rafts available.
E) The maximum quantity of the sailboats available.
F) The demand of raft trips that must be satisfied.
G) The demand of sailing lessons that must be satisfied.
3) What does constraint (6) represent?
A) The maximum number of captions who can be deployed.
B) The maximum number of crews who can be deployed.
C) The minimum revenue requirement.
D) The maximum quantity of the rafts available.
E) The maximum quantity of the sailboats available.
F) The demand of raft trips that must be satisfied.
G) The demand of sailing lessons that must be satisfied.

Answers

Answer:

1)  C

2) F

3) A

Step-by-step explanation:

Given that :  X = number of Wildlife raft Trips to be scheduled.

while Y = number of Group Sailing Lessons to be scheduled.

1) Constraint (1) : 120x + 160y ≥ 1800

Represents the Minimum revenue requirement

2) Constraint (4) : 6x ≥ 30

Represents The demand of raft trips that must be satisfied.

3) Constraint (6) : x + y ≤ 12

Represents The maximum number of captions who can be deployed.

Chloe runs the after-school cookery club.
The group will be baking 36 scones using the following recipe.
Recipe for 12 scones:
• 250 g self-raising flour
• 60 g butter
• 30 g caster sugar
• 175 ml milk
How much milk will be used?
ml​

Answers

Answer:

525 ml

Step-by-step explanation:

12 : 175 ml

36 : x

= 175 × 36

= 6300

x = 6300/12

= 525 ml

The amount of milk that is used while baking 36 scones will be 525 mL.

What are ratio and proportion?

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

Chloe runs the after-school cookery club. The group will be baking 36 scones using the following recipe.

Recipe for 12 scones:

250 g self-raising flour60 g butter30 g caster sugar175 mL milk

The amount of milk that is used while baking 36 scones will be given as,

⇒ 175 x 36 / 12

Simplify the expression, then we have

⇒ 175 x 36 / 12

⇒ 175 x 3

⇒ 525 mL

The amount of milk that is used while baking 36 scones will be 525 mL.

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

#SPJ5

Pls help - Solve for x​

Answers

Answer:

-3

3x/(x^2+6x) = 1 is this the qstn?

if so then the ans is -3

a horizontal line , such as y=4, has a slope of what

Answers

Answer:

0

Step-by-step explanation:

A horizontal line has a slope of zero and a vertical line has an undefined slope

2x+3y=10 8x+Ay=B
What Is the vaule of B

Answers

X-1/8 b-1/8ay hopefully this helps

How many lines of symmetry does this figure have?


Pls help

Answers

Answer:

4

Step-by-step explanation:

This figure has 4 lines of symmetry

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