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: 3. For each part, let {an} be the sequence with the given general term starting v Answer the…

A: As per our guidelines we can answer only 3 subparts of the given problem so kindly repost the…

Q: 6Th 11. Em-07R a) What is the first term and common ratio of the geometric series b) Does the series…

A: ∑n=0∞6n7n

Q: Find the n" term a, of a sequence whose first four terms are given. 9 10 11 -- -- 4' 8' 12' 16

A: Given:-84,-98,-1012,-1116,....

Q: Wi n=1 (-2)^ n! n^

A:

Q: Let (an) be a numerical sequence such that lim Ja," Then the radius of conver- 8. 71H00 gence of the…

A:

Q: Let Fn be Fibonacci sequence. Prove that:

A: By the definition of the Fibonacci sequence, Fn+2=Fn+1+Fn and the Fibonacci sequence is satisfied…

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

A:

Q: Discuss the Convergence a 2 e¹ M8 n=1 SH n

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. If a series Eu, converges to the sum u then so does any series obtained from Eu, by rouping the…

A:

Q: 1.) Prove that the sequence An= nt n In (2+1) converges to O. That is, prove limln (^+1)=0 nyo

A:

Q: 3. Build a power series with the interval of convergence [-1, 9). (Note: There are many possible…

A:

Q: Write out the first five terms of the sequence with, [(1-8)] determine whether the sequence…

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: Which of the sequences {a,} converge and which diverge: 1. a, = 2+ (0.1)" 2. а, 1+-

A: 1) an=2+0.1n We know that if -1<r<1 then limn→∞rn=0 So, limn→∞0.1n=0 Thus, limn→∞2+0.1n=2+0=2…

Q: I need the answer as soon as possible

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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

A:

Q: 7) The sequence an = 2ln (n+1). In (2n+1) a) Converges to 2 b) Converges to 1 c) Diverges d) None of…

A:

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: 2) is E=1 2n convergent?

A:

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

A:

Q: (-1)"62n+1 (2n+1)! А. 6 — 3! 63 65 * +...+ +... = 5! 7! В. 1 + (극)2 + (금)3 + (극)4 +…+ (금)" + … = +

A:

Q: 29. What is the 10th term of the harmonic 4 4 4 4 sequence 13’11’9’7'' ? ... [A] -5/4 [В] -4/5 [C]…

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: Q3) The sequence a, = 1 - (0.2)" a) converges to 0 b) diverges c) converges to e d) converges to 1

A:

Q: n2 + 5n + 2 Determine whether converges abso- (1+ )" lutely, converges conditionally, or diverges.…

A:

Q: Suppose Ec,(x– 1)" converges when x = 3 and diverges when x = -6, What can we say about the series E…

A:

Q: Is {-(n2)} n=1 to infinity, a convergent sequence in R with the usual metric?

A:

Q: 1- 5: Express the following as sequence of the indicated terms: 1 Ea, +- 1. 2' 10 а, 'i+1 2. 3.

A: "Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: (1) List the first 5 terms of oach of the soquence (a,). n+1 (d) an = sin An = 3n- - 1 3(-1)" (e) a…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

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

A:

Q: Whch of the following Showe the first 3 terms of the Taglor sena expansion for about X> 2 ? A. *:1-…

A: Given, f(x)=1x we have to determine the first 3 terms of the taylor series expansion forgiven f(x)…

Q: 9) n+3"

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

Q: 33. Use the Squeeze Theorem to prove (sinn/n} c) {3"/n!} b) fn/2"} f by contradiction. a)

A: 33.) use squeeze theorem to prove that each of the following sequences converges a) sinnn  , (b)…

Q: 2n 18. а, 1+ %3D n

A: Note:

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: 1 Find the limit of the sequence n %3D 8, а. b. 1 с. 0 d. 1 e. The limit does not exist. -/2

A: limn→∞1n9/2The limit of the quotient is the quotient of limits:=limn→∞1limn→∞n92The limit of…