Mathematics High School

Use the geometric series f(x) = 1/1 - x = sigma^infinity_k = 0 x^k, for |x| < 1. to find the power series representation for the following function (centered at 0). Give the interval of convergence of the new series. g(x) = x^3/1 - x Which of the following is the power series representation for g(x)? A. sigma^infinity_k = 0 x^3/x^k C. sigma^infinity_k = 0 1/1 - x^k + 3 B. sigma^infinity_k = 0 x^k + 3 D. sigma^infinity_k = 0 x^3k The interval of convergence of the new series is. (Simplify your answer. Type your answer in interval notation.)

Answers

Answer 1

B. sigma^infinity_k = 0 x^k + 3, and the interval of convergence is (-1, 1).

To find the power series representation for g(x), we need to rewrite g(x) in terms of the given geometric series.

Notice that g(x) can be written as:
g(x) = x^3/1 - x = x^3 * (1/1-x)

We can now substitute the formula for the geometric series to get:

g(x) = x^3 * sigma^infinity_k = 0 x^k
= sigma^infinity_k = 0 (x^3 * x^k)
= sigma^infinity_k = 0 x^(k+3)

Therefore, the power series representation for g(x) is:
sigma^infinity_k = 0 x^(k+3)

The interval of convergence of this series is the same as that of the geometric series, which is |x| < 1.

In interval notation, this can be written as (-1, 1).

Therefore, the correct answer is B. sigma^infinity_k = 0 x^k + 3, and the interval of convergence is (-1, 1).

Know more about convergence here:

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Related Questions

The length of a rectangle is 5cm and the width is 3cm. What is the length of a diagonal? Leave the answer in reduced exact form. Hint: Draw A PICTUR



​

Answers

Answer:

[tex]\sqrt{34} } =5.83[/tex]

Step-by-step explanation:

[tex]D=\sqrt{5^{2} +3^{2} } =\sqrt{34}[/tex]

Write the following inequality in slope-intercept form. –12x – 2y ≥ –42 y ≥ –6x – 21 y ≤ –6x – 21 y ≤ –6x + 21 y ≥ –6x + 21

Answers

Answer:

y ≤ –6x + 21

Step-by-step explanation:

Silas and Lilly attended a math conference. The total registration fee was $327.50. If each person paid the same amount, which equation
represents the amount each person paid?
A 2x = 327.50
B 1/2x = 327.50
C x + 2 = 327.50
D x - 2 = 327.50

Answers

Answer:I think the answer is letter B.

Step-by-step explanation:

What is -2 1/3 - (-5)?

Answers

Answer: =2  2/ 3

Step-by-step explanation:

Please help I don't know how to do this

Answers

i not sure but i think its  183

Answer:

question 18 asking for a equation for each week 89÷4

question 19 would be 60 + 123 = 183 then 183 ÷ 4 = 45.75

Solve the equation. 8w = 48​

Answers

Answer:

8w=48

This answer can be simplified by dividing both sides which contain the variable, which in this case is 8. Dividing 48 by 8 gets 6. This means that w equals 6.

Answer:

w = 6

Step-by-step explanation:

Solve

8w = 48

8w/8 = 48/8

= w = 6

SOMONE HELP PLEASE! I HAVE BEEN STRUGGLING ALL DAY!

Answers

Answer: 378 the second option

Step-by-step explanation:

Answer:

378

Step-by-step explanation:

Multiply 9 and 12 then divide by 2 to get the area of the triangle then multiple by 7 to get the volume

The circumference of a circle is 5 feet. What is the area?
Give the exact answer in simplest form.

Answers

Answer:

We have the formula for the area of a circle: S = R² x [tex]\pi[/tex]

=> S = 5² x 3.14 = 78.5 f²

Step-by-step explanation:

PLEASE HELP! WILL MARK BRAINLIEST IF U ANSWER CORRECTLY! IF WRONG U WONT GET IT

Answers

Answer: 120cm

Step-by-step explanation:

John joined a gym for 6 months. He pays 20$ per month plus a membership fee. If his bill is 150$, what was the membership fee?

Answers

Answer:

Step-by-step explanation:

If he's been at the gym for 6 months, and he is charged $20 each month, then he has paid $120 dollars, not counting his membership fee. His total bill is $150.

150-120= $30

His membership fee was $30.

Hope this helps!

Mark Brainliest plz!

x is the number of months and y is the membership fee

[tex]cost = 20x + y[/tex]

[tex]150 = 20(6) + y[/tex]

[tex]150 = 120 + y[/tex]

[tex]150 - 120 = 120 - 120 + y[/tex]

[tex]30 = y[/tex]

The membership fee was $30.

a coin is tossed several times and the ratio of the head to tails is 24:26. What Fraction of Tosses are heads?

Answers

Answer:

siiiiiiiiii

Step-by-step explanation:

What is the equation graph below?

Answers

Answer: y =7/4x

Step-by-step explanation:

The y-intercept is 0. To find the slope, do the change in y over the change in x. At the point on the graph, there is a slope of 14/8 = 7/4

9. An inequality is shown
2x - 5 < 33
Select all the values that are solutions to this inequality
a. 28
b. 26
C. 19
d. 18
e. 12

PLEASE HELPP!!

Answers

The answer is c 19
38/2=19
Step-by-step explanation
The answer is d. 18 and e. 12.

Explanation:

2x - 5 < 33

2x < 33 + 5

2x < 38

x < 38/2

x < 19

x must be smaller than 19.

It can’t be 19 because it didn’t say smaller than or equal to.

So the answer is 18 and 12.

(2x2)+(6x 109)
I don’t know how to do this

Answers

Answer:

658

Step-by-step explanation:

4+654=658.........

Answer:

658

Step-by-step explanation:

First solve 2x2, which is equal to 4.

Then solve 6 x 109 which is equal to 654.

Now add 4 to 654, and you'll get 658

determine if f (x) = - x^3 + 4x^2 +7x - 6

Answers

-x(x2-4x-7)+6=-x(x2-4)-7+6=-x(x+2)(x-2)-1=-x-1

Today, everything at the store is on sale. The store offers a 20% discount. The regular price of a T-shirt is $16. What is the discount price?

Answers

Answer:

12.8

Step-by-step explanation:

I think it is $14 or $4 one of those I did 20-16=4 but I’m not sure if it is - or times if it is times it will be $14 good luck:)

what times 1,000 equals 4,320

Answers

Answer:

4.32

Step-by-step explanation:

Call the unknown number = x

We have: 1000x = 4320

=> x = [tex]\frac{4320}{1000}[/tex] = 4.32

=> The number we need to find is 4.32

Answer:

4.32

Step-by-step explanation:

Find the length of side a.
10
A
6
A. 4
B. 64
C. V 136
D. 8
PREVIOUS

Answers

Answer:

D .8

Step-by-step explanation:

hypotenuse (h) = 10

base (b) = 6

perpendicular (p) = a= ?

We know by using Pythagoras theorem we get

p = √ h² - b²

a = √ 10² - 6²

a = √ 64

a = 8

Hope it will help :)

It takes lucas 3 hours to cycle from his home to his friend's village. But if he travels 5 mph slower, it will take him 1.5 hours longer. How far is the friend from lucas' house

Answers

Answer:

Step-by-step explanation:

It takes Lucas 3 hours to cycle from his home to his friend’s village:  

3 hours • (a certain speed) = distance in miles  

If he travels 5mph slower, it will take him 1.5 hours longer:

4.5 hours • (the same speed - 5mph) = the same distance in miles

 4.5 • (x - 5) = 3x

4.5x - 22.5 = 3x

1.5x = 22.5

x = 15mph  

3hours • 15mph = 45 miles

What fraction do you multiply 3 by to get 1

Answers

the answer is 1/3

1/3 + 1/3 + 1/3 equals 1

which is the same as 1/3 times 3

por liquidación,toda la ropa de invierno está en oferta,te descuentan 50 pesos por cada 100 pesos que compres ¿cuanto se deberá pagar por una chamarra cuyo precio y otal es de 850 pesos?​

Answers

Answer:

no comprendo

Step-by-step explanation:

Please Help i need this right now Thanks

Answers

60° i think but i’m not sure

If the lines in a system of equations have different slopes and the same y-intercept, how many solutions does the system have?

Answers

Answer:

289819

Step-by-step explanation:


HELP ASAP DUE IN 20 MINUTES

Answers

Answer:

x = 3

< D = 26

< E = 54

Step-by-step explanation:

I did the math

6/1000 as a common fraction

Answers

This question isnt rlly descriptive but 6/1000 could be 3/500?

help plsss how do you find the size of angle ABE​

Answers

Answer:

∠b = 90°

Step-by-step explanation:

If you wrote it correctly then ∠d will = 90°, right?

We have AB ║(which is parallel to) D => ∠b = ∠d = 90°

P/S: I think that you took the wrong photo, the right question should be above. I'm very please if you can take it again and I will write the right solution down below in the comment section (if u don't mind)

Find the area of a triangle with:
b: 14 cm
h: 23 cm
ANSWERS
322 cm2
322 cm3
161 cm2
161 cm3

Answers

Answer:

161cm2

Step-by-step explanation:

Area: 1/2 x base x height

1/2 x 14 x 23=161

Area is measured in cm2

Hope this helps!

x is an even whole number less than 5.​

Answers

Answer:

x can either be 2 or 4

Step-by-step explanation:

Whole numbers less than 5 are = 1, 2, 3, 4

Even whole numbers less than 5 are = 2 and 4

1 and 3 are odd numbers

Therefore, even whole number less than 5 are 2 and 4

x can either be 2 or 4

Perform the indicated operation.
f (x) = x2 − 4 g(x) = −3x Find f (g(x))

Answers

Answer:

-6x-4

Step-by-step explanation:

2(-3x)-4

-6x-4

r F(x) is your frame function since it is on the outside, when every you get to an x in the F function you plug in the G function then solve as normal.

pls help me solve surds , √75 ,√48, √12,√125,√28. pls help​

Answers

√75 = √(5²×3) = √5² √3 = 5√3 = 8.66

√48 = √(4²×3) = √4² √3 = 4√3 = 6.93

√12 = √(2²×3) = √2² √3 = 2√3 = 3.46

√125 = √(5²×3) = √5² √3 = 5√3 = 11.18

√28 = √(2²×7) = √2² √7 = 2√7 = 5.29
All the answers are rounded off to the nearest hundredth.

√75 = 5√3 = 8.66

√48 = 4√3 = 6.93

√12 = 2√3 = 3.46

√125 = 5√5 = 11.18

√28 = 2√7 = 5.29
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