(6) (:) n Show that for n > 0. n

Q: limit as n approaches infinity of (1-n)/(3n+5)

A: Let's find.

Q: 2n2 +n+2 ii. Use the result in (i) to test for convergence = 1 5n3 + 3n

A:

Q: Find the radius of convergence and the interval of convergence. k (x + 3)* k=0

A: The summation of (5/7)k (x+3)k ; k from 0 to infinity.

Q: find the interval of convergence.

A: Apply ratio test and check weather series is convergent or divergent.

Q: 9. Find the limit (if it exists) of the sequence (x_n) where x_n= n-3n^2.

A: Given xn=n-3n2

Q: an Q4. If £ an converges and an > 0 for all n , can anything be said about E- ?

A: Given that ∑an converges and an>0 for all n. The objective is to determine whether ∑1an converges…

Q: 5. Find all values of x >0 so that ) converges. 3k k=2

A:

Q: 4. Find the radius of convergence and interval of convergence for the following. (х — 2)п 2n (2n)!…

A:

Q: What are all of the values of x ,such that Σ (3x)" (-1)"+ 00 converges? n=1

A: To solve this question we shall use root test for series.

Q: -n =1 5n3 + 3n iii. Use the result in (i) to test for convergence 2n=1 Vn? +5

A:

Q: 1. Find the Interval, Radius and Center of Convergence. n 2n n=0

A: As per our guidelines we supposed to solve the very first question when multiple questions are…

Q: Find the radius of convergence for: (n!)* (3n)! n=1 1

A: Given :

Q: Find the interval of convergence. (x + 5)" Σ (n In(n))² n=2

A: To Find: Interval of convergence of given series…

Q: limit as n approaches +infinity of (n/(e)^n)

A:

Q: Find the radius and the interval of convergence of  ∑∞n=1  (3^n*(2-x)^n)/(n+1)

A:

Q: Find all values of x such that converges. n! n=1

A: Given that, series ∑n =1∞  xn2n! Compare the series ∑n =1∞  xn2n! with its standard form ∑n =1∞  an…

Q: 4) Find the interval of convergence (x-2)" 8". n of n=1

A:

Q: (x+2)" Find the interval of convergence for 2 n²(-3)" n=1

A:

Q: (x – 5)" - 10. Determine the interval of convergence of n2 n=1

A:

Q: 7. Find the radius and interval of convergence. (л — 2)" a) > (x + 1)" b) n 3n+1 nº 5n n=1 n=1

A:

Q: Find the sum from k=1 to infinity of: [5/(3k+1)] using the limit comparison test.

A: Limit comparison Test:

Q: Find all values of x such that ΣΗ converges. n! n=1

A:

Q: Find all values of x for which ) (3x)" converges. n=D1

A:

Q: ∞ Find the interval of convergence for n=1 The interval of convergence is a E (x − 4)" n² 3n

A:

Q: 1 diverges by comparing with n-. 16. Show that n² – 3 n=2 n=2

A: Given: The series ∑n=2∞1n2-3 To show: The given series converges by comparing with ∑n=2∞n-1.

Q: Find the interval of convergence: n³ (x + 5)" 6n n=1

A:

Q: 01. A gardener was observing thd behavior of the roses that he transplanted a week ago. He observed…

A: ANSWER :

Q: 1) Determine the interval and radius of convergence of (x-2)" (n+1)5*** 8. Σ n=0

A:

Q: Find the interval of convergence of x3n+2 Σ In(n) n=2 (Use symbolic notation and fractions where…

A:

Q: 14. What does it mean that a sequence {xn} tends to infinity?

A: What can we say if the sequence tends to infinity .

Q: E (1- nsin-) converges n = 1

A: Series convergence test problem.....

Q: How do you find the sum from k=1 to k=infinity of 2k/(k+7k) using the limit comparison test?

A:

Q: (x + 2)" Find the interval of convergence for 22(-3)n n²(-3)" n=1

A:

Q: 2. (a) Use the definition of the derivative and the Binomial Theorem to = nx"-1 for any x" is f'(x)…

A: Since you have asked multiple question, we can solve first question for you. If you want other…

Q: 3n 4. Use the ratio test to determine whether Σ converges. (n + 1)! n=1

A: use the ratio test for convergence of series.

Q: Find the convergence set (or interval of convergence) for the 80 (x-2) Σ 6n+8 n=0 1.

A: Solution

Q: 2. (a) For n ≥ 0 and x E R, prove that (b) Prove n n Σ ^ (^.) 2^* (1 - 2)"-* k k=0 = = In. n x)n-k…

A:

Q: (-1)" Σ Find the interval and radius of convergence for: k" n=0

A:

Q: 3n? is increasing. Find an upper bound. n2 +2 Show that an

A: Consider the sequence and check whether Sequence is increasing or not.

Q: The interval of convergence of (-b)" x"*1 where b > 0; is n+1

A:

Q: 26. The interval of convergence for (X-3)* k - (x– is а. (-3, 3] b. [-3, 3] с. (-2, 4) d. [2, 4] е.…

A:

Q: 5). Find the interval of convergence. ∞ n = 0 xn n7 + 8

A: Introduction: A power series can either be convergent everywhere or can be convergent over a…

Q: 2n2 +n+2 Σ ii. Use the result in (i) to test for convergence = 1 5n3 + 3n

A:

Q: x" n n=0 n2

A:

Q: 3. Determine the radius and interval of convergence of 8 k=2 7k (x - 5) k k

A:

Q: the interval of convergence. (x+7)" ( a) Σ In n=1 x" (b) En! n"

A:

Q: 5) Find all values of x for which En=1 nxn (n+1)(2x+1)n converges absolutely.

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Q: Find the interval of convergence for  ∑∞ n=2 (x^n)/((n^2)(3^n))

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Q: k2 Use the integral test to determine whether 2 1319)2 converges. (k3 + 9)2 k=1

A: