Q#5. 8. 1 a) Show that the series > is convergent. (n+3)n+4) n=1 n+3 b) Apply the Ratio-Test to discuss the convergence of the following series 7"-2 n=1

Q: Show that the series Ln=l 12+2z10n-5z"ª –3z+2;10n converges absolutely for |리 < 1.

A: The series ∑n=1∞an is absolutely convergent if the series ∑n=1∞an  Ratio test:  The series ∑n=1∞an…

Q: 9-) Find and test the partial sum of the given series it for convergence : n=1 (₁^) (2+0+ (-1)^ 2^

A:

Q: 11) 3".Zn

A:

Q: What is the largest interval of convergence of the power series (3z+1)" 2n+1 n=1

A:

Q: (8x – 7)" Find the interval of convergence of the power series : 23n

A:

Q: b) Determine the convergence interval (with endpoints) of the following series: (x – 1)" 2"(n + 1)…

A:

Q: Prove that the resulting series when x = 0 is conditionally convergent in the power series +00 (3x -…

A:

Q: 12' >(- 1)"-'b. where b = n' 1=1 (n+2) 14"+3 a) Find and simplify bn+1 "q b) Test the given series…

A:

Q: What does the series LIin (4)]" (2")n! 2. converge to? Use your knowledge from 6.5 to answer this…

A:

Q: Please check this for me

A: Step 1:Step 2:Step 3:Step 4:

Q: Find the interval of convergence of the power series

A:

Q: 1)Which of the series given below converge absolutely? Conditionally converges? Divergent? Explain…

A: It is given that the series ∑n=1∞-1n+1nn2+1. Check the series ∑n=1∞-1n+1nn2+1 is absolutely…

Q: Q-4) Determine if the following series is convergent or divergent: 1 5* integral test n (Inn)² Zn=2…

A: Solution

Q: Consider the power series 80 an (x – 6)" n=1 of variable x and with (a some sequence. If it is known…

A: In this series we have to find whether the series is convergent of divergent.

Q: ) Consider the power series * (-1)"(4x + 4)" yn +5 Find the center and radius of convergence R. If t…

A:

Q: 25) Σ 5" (2n-1)! Ln=2 n-(2n+1)!

A:

Q: 00 A) > n! x" is convergent for x = n=1 00 B) E n! (10x – 8)" is convergent for x = n=1 C) The…

A:

Q: 8. Which of the series converge, and which diverge?: n+1 (2) Σ S 3 (c) 1 1 + ln²n (Inn)² n³ (d) n 1…

A: Disclaimer: Since you have posted multiple sub parts of question , we will solve first three sub…

Q: 11) E1 COs ()

A: As per bartleby guidelines we only give first question answers.

Q: find the interval of convergence in the power series and include a check for convergence at the…

A:

Q: 2n +1 a) n=1 3n-5 WE

A: Solution:Given  ∑n=1∞ 2n+13n-5To find the nth term test say about the convergence of the series.

Q: 7. Determine the interval of convergence of the series n=1 * (x+ 2)" Σ n 3" Show the work that leads…

A:

Q: Q2/ A) Determine if the following series is convergent or divergent 2n En=1 3n n! n! En=1 (2n) 00

A:

Q: (n+1)lz" is 00 The Interval of convergence of the power series -1 Select one: O non of them o (-0,…

A:

Q: * 3" +n 2) Use the Comparison Test to determine whether the series or divergent. Show All Your Work.…

A:

Q: Find the interval of convergence of the power series, where k is a positive integer D Σ n = 1…

A: Find the interval of convergence of the power series, where  is a positive integer