1. Examine the series for convergence (-1)" n· 3n

Q: Determine the convergence or divergence of the series.

A: We have to find out            ∑n=0∞(1.075)n convergent or divergent

Q: 2. Investigate the convergence and divergence of the following series, and obtain the sum upon…

A:

Q: Find the radius of convergence and interval of convergence of the series. (x – 6)" 72 nš +1 n=0

A: we have to find R and I

Q: en I) Find the set of convergence of the series (x – 1)". n+1

A: As you are given multiple questions I solved only first.

Q: Does the series from 1 to infinity of (2^k*k!)/((k+2)!) converge or diverge?

A:

Q: Σ -(2.r – 1)3". 14+1

A:

Q: Σ (n:)? The radius of convergence of the series (x- 2)2 is equal to ........ n=1 3" (2n) !

A:

Q: Find the interval and radius of convergence for the following power series: n(x– 2)" 5"

A: Consider the provided question, We have to find the interval and radius of convergence of the given…

Q: Find the radius of convergence and interval of convergence of the following series. n (x - 9)" n3 +1…

A: By using formula of radius of convergence and find way interval of convergence

Q: 00 The interval of convergence for the power series (-1)"(x + 3)" -is n· 3" n=1

A: First, find the radius of convergence R and by using it we can define the domain of convergence and…

Q: Find (with justification) the interval and radius of convergence of the power series: > Σ (n+1) n=2

A: We have to find

Q: (-1)" (х — 2)" 00 (п +1)* n=1

A: For the solution of the problem follow the next steps.

Q: Explore the absolute and conditional convergence of the series In n Cos n=1 iM:

A:

Q: Find the radius of convergence and interval of convergence of the series. 00 (8n)! n=0 R = I =? v ?…

A: Given series is

Q: 2. Investigate the convergence and divergence of the following series, and obtain the sum upon…

A: Given series is convergent by comparison test.

Q: 1. Investigate the convergence and divergence of the following series, and obtain the sum upon…

A: We know

Q: Determine the convergence or divergence of the series

A: To find the series is convergence or divergence.

Q: Find the radius of convergence and the interval of convergence for the power series E(-1)» (8 – a)"…

A:

Q: Find the radius of convergence and interval of convergence of the series. n°r" (-1)" 4" R = I =

A:

Q: ind the radius of convergence and interval of convergence of the power series 10"x" n3 n=1

A:

Q: Determine the interval and radius of convergence for the power series. LE 2k (x + 2)* k=1

A:

Q: (4-x)". /n 00 n+5 9n : 7" n=1

A:

Q: 8. Find the radius of convergence and interval of convergence of the series Eo (а-2)" n2+1 n=0

A:

Q: 00 (-1)" Ln-1 n п — n=2

A:

Q: Find the radius of convergence and interval of convergence of the series. 2n E(-1)" (5n)! R = ?v I…

A:

Q: h=2 n-1

A: Given:          The series is ∑n = 2∞nn - 1   Comparison Test:  Consider the two positive term…

Q: 1. Investigate the convergence and divergence of the following series, and obtain the sum upon…

A:

Q: У7-"(10т — 1)" —п n=0

A:

Q: (d) Find the interval of convergence and radius of convergence of the power series 00 k! k=0

A:

Q: (b) n 1+ (x-1)"; r=1/e Σ(1-1) η n=1

A: Here, the given series is: ∑n=1∞1+1nn2(x-1)n Let, an=1+1nn2(x-1)n; n≥1

Q: 12. Find the interval and radius of convergence of the series k=1

A:

Q: Find the radius of convergence and interval of convergence of the series. (-1)"-1 „"+4 n=2 R = I =

A:

Q: 10. Determine the interval and radius of convergence for the power series. 2k (x + 2)k k=1

A:

Q: b. Find the interval and radius of convergence of the given series 27 (х — 3)" n2 n=1

A:

Q: 11) Find the radius and interval of convergence of (x + 3)" Σ the series n = 1 n!

A:

Q: Find the radius of convergence and interval of convergence of the series. 9"x" n=3 R = I = |? V ?V

A:

Q: Find the radius of convergence and interval of convergence of the series. (x – 4)" 72 E(-1)" Зп + 1…

A:

Q: Find the convergence radius and convergence interval of the next series 14. Σ (-2)" √n (x+3)" n = 1

A: Problem is solved using concept of convergence.

Q: Find the radius and interval of convergence, R, of the series. E-1 n!

A: Answer is in below step.

Q: Find the radius of convergence, R, of the series. Σ Зп — 1 - n = 1

A: Explanation of the answer is as follows

Q: Find the radius of convergence and the interval of convergence of the power series. 4"(r – 1)" n=1

A:

Q: Find the radius of convergence and interval of convergencE of the power series. (x 25. E 2)" n=1 n"

A:

Q: 4) Determine the centre, radius, and interval of convergence of the following series Że(4-x)".

A:

Q: Σ (-1)"+12"(x+1)" n3n n=1

A:

Q: Find the radius of convergence of the power series. 00 E(-1)"n+ 9 n = 0

A:

Q: Find the radius and interval of convergence of the following series. n +1 7n=1

A:

Q: 00 Determine the radius of convergence of the power series > (x – 2)". n=0 = i

A: Use the ratio test to find the radius of convergence of the power series ∑n=0∞(x-2)n Ratio test:…

Q: Find the radius of convergence, R, of the series. Σ 5"n2x" n = 1

A: The given series is: ∑n=1∞ 5nn2xn Therefore: an=5nn2xn