3. The value(s) of b for which the series E=50 is convergent are: 4 n3b2 B)는 C)- D)- (수-w-) n (") (M E) None of them.

Q: The sequence

A: We use ratio test to prove convergence or divergence here.

Q: Do the following sequences {a} converge or diverge? Justify your answers (a) an 3" (b) an - (-1)"/ñ…

A: Explanation of the answer is as follows

Q: 4. Assume that Achilles' speed as 100 times as fast as the tortoise's and that this animal has been…

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Q: Suppose that 2-o Cx" converges when x = -4 and diverges when x6. What can be said about the conver-…

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Q: 11) 3".Zn

A:

Q: If 2 a, is convergent with positive terms n=1 is it true that sin (a,) is also n=1 convergent?…

A:

Q: 05:A) Suppose La, converges. Show that {(1+=)* a, Converges. B) Let E a, and b, be absolutely…

A: (A) Given that converges. And to show that converges. And it is known that, converges. So, it is…

Q: Which of the following assertions is true for the given sequences? a) {(-1)" e"} converges п+1 b)…

A: If you like the solution then please give it a thumbs up.... The Answer is:           Result :…

Q: In the givn equation as folows ,  state where the power series is centered:-

A: Given: ∑n=1∞-1n2n-12nn!xn Concept Used: Consider a power series ∑n=1∞anx-an Here 'a' is the center…

Q: Given the sequence Of (n)=2+2 Of (m) = 2 + 1/ n Of(n)=n+: 1+n Of (n)=3--1/ = 21/1, 23, 2441... what…

A: The given sequence is 212, 213, 214,... The objective is to find f(n). A map from ℕ to ℝ defines a…

Q: QUESTION 7 3" -1 Find the exxact sum of the series if it is convergent. If it is divergent write…

A: Use geometric progression

Q: 6) Which of the following series converges? 2n²+n+1 n²+1 a) En-o b) Emo (4)" (-)" d) None of the…

A:

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

A:

Q: 58. Which of the following sequences is/are not convergent? I: a, := n+1 3n2-4 ,n 2 1 II: a, := n+1…

A:

Q: . Let an = sin sin for n eN = {1, 2, 3,...}. n+1 (a) Determine if the sequence {an}n=1 converges or…

A:

Q: ㅋ. for neN. Does (xn) have a convergent sub. (gn) have a convergent subsequence? If you are unable…

A: Statement : Every bounded sequence of real numbers has a convergent subsequence.

Q: B){(sin(x))/x

A:

Q: Find the interval of convergence of the power series: E (x- 3)"-1 (-1)" 72 a) (-1, 1] b) [2, 4] c)…

A: Use ratio test for checking the convergence

Q: quence (x₂) satisfying A sequence 1 0≤x≤. n where Σ(-1).x, diverges.

A: Given that the sequence xn satisfying 0≤xn≤1n. We have to determine whether the series ∑-1nxn…

Q: 12. Prove the following facts about the Fibonacci sequence (Fn): (1) (Chapter 10, #26) E-1 F =…

A: Given, The Fibonacci sequence (Fn) Fn=Fn-1+Fn-2, where F0=0 & F1=1

Q: Suppose that the series c, x" has radius of convergence 8 and the series d,x" has radius of…

A: The given two series ∑cnxn and ∑dnxn whose radius of convergence are 8 and 9 respectively. Calculate…

Q: disprove thato Let M=(o,1]SR. Then in S" Convergent sequence and tyo prove or

A:

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: Converges or diverges

A:

Q: 4. Assume nana"- + 2 anc" = 0. =D0. n=1 n=0 Determine {an} and the series n=0

A:

Q: 32. Find the limit of the series: x (1+x) (+x) 1+x2 A) B) xx X+x C) (1+x D) (1+x) E) x

A: Given series is,

Q: Prove the following sequences diverge. (-5)"т + 3 2 sin ( 10"T + 4 en +n? +n +11 (Ъ) » (* ) 2n n -

A: We use basic of sequence.

Q: 3" 29. The series (x-2)" is convergent on the interval: (03) A) 5 7 B) 3 3 5 7 C) 3 3 5 7 D) 5 7 E)…

A:

Q: trig nometrie s converges unitoomy. Fo wier eres series [-a 9 then it is a on

A: We have to prove the statement, that if a trigonometric series converges uniformly on -π,π then it…

Q: n In(n) n=1 is this Series Con lerges for my12?

A:

Q: 4. Suppose (xn) converges, and let K be a positive integer. Now create a sequence (yn) by changing…

A:

Q: The sum of the series n2n+1 -1)" 9n+1(2n)!

A:

Q: Use de Moivre’s theorem with n = 4 to prove that cos(4θ) = 8 cos^4 (θ) − 8 cos^2 (θ) + 1

A:

Q: 9) n+3"

A: Comparison test for series of positive terms states that, If an, bn are two series such that…

Q: 1) (-1)*- n² 2" n=1 a) Show that the series is convergent. Show All Your Work!

A: