Test the series for convergence or divergence. You must justify your answer with the correct method: (You must quote the name of the method) n2 - 1 (-1)". n3 +1 n=1

Q: Find the radius of convergence of the power series. (-1)^n!(x – 9)" 2" n = 0

A:

Q: Find the radius of convergence and interval of convergence of the series. (-1)" x"+6 n +1 n=2 R = I…

A: ∑n=2∞ -1nxn+6n+1

Q: Find all the values of x such that the given series would converge correctly.

A:

Q: Find the radius of convergence of the power series. (If you need to use o or (-1)" x" Σ 2" n = 0

A:

Q: Find the radius of convergence of the power series. (If you need to use co or -0o, enter INFINITY or…

A:

Q: Find the radius of convergence of the power series. (If you need to use co or -oo, enter INFINITY or…

A: Given ∑n=0∞-1nxn8n

Q: Vn3+1

A: (A) Let un = 1/sqrt(n3+1) and vn = 1/n3/2 Then {vn} being a p-series with p = 3/2 > 1 is…

Q: Find the interval of convergence and the radius of convergence of the power series (х -4)" n=1 n.9"

A:

Q: Find the interval of convergence of the power series - 2)" | n =1 h

A: Given problem:-

Q: Find the radius of convergence and interval of convergence of the series. an+3 Σ 4n! n=3 R =

A:

Q: Find the radius of convergence of the power series. (If you need to use co or -0o, enter INFINITY or…

A:

Q: Find the interval of convergence of the series, (x – 2)" n3 n=1

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The radius of convergence of the series 00 n! (3x – 1)" -

A:

Q: 1 converge? What are the values of x that would make the series

A:

Q: Find out whether the series given below converges or diverges. 1 4vn + \n_

A: Solution :- First we will see one series test. COMPARISON TEST(Limit form): Let ∑n=1∞an  and ∑n=1∞bn…

Q: Find the radius of convergence of the power series. (If you need to use o or -0o, enter INFINITY or…

A: Radius of convergence of a series ∑n=0∞akxk is 1lim sup |ak|1k Here we have an=(-1)n4n Let c=lim sup…

Q: Find an easy expression for the sum of the series on its interval of convergence. (-1)"-'n -x" 2"…

A: Given series is ∑n=1∞-1n-1n2nxn

Q: Test the series for convergence or divergence. 4" Σ 3n + 7" n=1

A: Given:

Q: Test the series for convergence or divergence. (-1)^+1 n+8 n=0

A:

Q: Find the radius of convergence of the power series. (If you need to use ∞ or -oo, enter INFINITY or…

A: A power series is given by, ∑n=0∞-1nxnn+6. The objective is to find the radius of convergence of the…

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: Š (-1)" x" n - 0 2"

A: Radius of convergence for series ∑n=0∞an(x-c)n is given by 1R=limn→∞an+1an

Q: Find the radius of convergence and interval of convergence of the series. (-1)"x"+4 n +7 n=2 R =

A:

Q: n! 11) E 100 n%=D1 5n 72

A: The given series is: ∑n=1∞  n!5n

Q: By using a suitable test determine whether the following series converges or diverges, give a reason…

A:

Q: Find the radius of convergence of the power series. (If you need to use co or -0o, enter INFINITY or…

A:

Q: Find the positive values of p for which the series converges. (Enter your answer using interval…

A: See the attachment

Q: Find the interval of convergence and the ratio of convergence for the series Σ 3n(x-3)n/(n+3)!

A: Given  The series is ∑n=0∞3nx-3nn+3! .   Limit ratio test :- limn→∞an+1an=L if L <1  then ∑n=0∞an…

Q: 1 k=1 Vk8 + 2

A: ∑k-1∞ 1k8+251k8+25<1k851k8+25<1k85∑k-1∞1k8+25<∑k-1∞ 1k85

Q: By using a suitable test determine whether the following series converges or diverges, give a reason…

A:

Q: Find the radius of convergence of the power series. (If you need to use o or -0o, enter INFINITY or…

A:

Q: Find the radius of convergence of the power series. (If you need to use oo or -0o, enter INFINITY or…

A:

Q: +o0 E(-1)" n=2 n?

A:

Q: Find the radius of convergence and interval of convergence of the series (-3)"x" √n+1 n=0

A: For a given series of the form ∑anFor radius of convergence   we will find first limn→∞an+1an<1…

Q: Find the radius of convergence of the power series. (If you need to use ca or -co, enter INFINITY or…

A:

Q: Find the radius of convergence and interval of convergence of the series. (-1)" x"+4 n+5 R = I =?

A:

Q: Which of the series converge absolutely, which converge conditionally, and which diverge? Give…

A: Given that : The series ∑n = 1∞ 1n .

Q: The interval of convergence of the power series below is (-1,1) x" п n=0

A: We have to find interval of convergence

Q: Does the series 2(: - ) n=1 \N converge or diverge? Justify your answer.

A:

Q: The question asks to find the​ series' radius and interval of convergence and find the values of x…

A:

Q: Find the interval of convergence for the given series. Also, find the sum of the series, (x – 5)" 2"…

A:

Q: Does the series sum_(n=1)^(infty ) (5n^(2)+7n+12)/(8n^(2)+17n-1) converge or diverge? Write the test…

A:

Q: Find the radius of convergence of the power series. (If you need to use co or -0o, enter INFINITY or…

A:

Q: Test the series for convergence or divergence. (-1)"-1 T"

A:

Q: Test the series for convergence or divergence. -1 sin? n n+ 37

A: Given

Q: Find the radius of convergence of the power series (-1)* (x – 6)" 20" n4 n=1 Your answer should be a…

A:

Q: Test the series for convergence or divergence. , n2 n =D1 n+1

A:

Q: Find the radius of convergence and the interval of convergence of the series. (-1)" (2n – 1)2" (x –…

A:

Q: -3 (а) 2*/2 k=1

A: see below the answer we will use the ratio test