Which of the followings are true? 1. E (-1)" is absolutely convergent. m-D1 n+inn II. En-1 2" (-1)8r is conditionally convergent. III. (-1y"-1 is conditionally convergent. IV. En-l (-i"n is conditionally convergent. n+? O a. II, IV O b. I, II

Q: Which of the followings are true? 1.En=1 7?+Inn (-1)" is absolutely convergent. II. >n=1 (-1)m is…

A:

Q: Which of the followings are false? I. 0 (-1)" is absolutely convergent. Ln=1 n² +Inn 2n II. E (-1)…

A: we have to check each options

Q: (a) (². ¹) If the sequence (an) is defined by the recursive formula an+1 = -2-a, a₁ = 1, then (an)=1…

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

Q: Which of the followings are true? 1. E is absolutely convergent. 00 n=1 n! II. En-1 (-1)-1 is…

A:

Q: Which of the followings are false? 1. E (-1)" Ln-1 n+ Inn is absolutely convergent. 2n (-1)* 2…

A: We have to choose the correct answer

Q: Determine the sum of the series e +e2 +e3+ .. if it converges. O diverges. e A Moving to the next…

A: Given query is to find sequence converging or diverging m

Q: 3 a, +2 A sequence of real numbers a, is defines inductively as a1 = 1 and an+1 n 2 1. an+3 Use this…

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Q: Which of the followings are true? (-1)" 1. En-1 n²+Inn is absolutely convergent. (-1)* II. En-1 is…

A: We have to find the option

Q: Problem 3. For what values of c does the series 1 C Σ√n²+4, n+2 n=1 converge? (Hint: use the…

A:

Q: Which of the followings are false? 1. E0 (-1)* m%=D1 2+irn is absolutely convergent. (-1)2. is…

A: which of the following is false

Q: The. negation of (an) convergent is: a. Va, 3V, VN,3n > N: an € V b. 3a, VV,3N, Vn 2 N: an € V c.…

A:

Q: Match each of the following with the correct statement. C stands for Convergent, D stands for…

A: Concept used: Divergence: When the values goes to -∞ or goes to ∞ that is it does not approach one…

Q: Let an > 0 and assume that an diverges. Write Sn = a1 +a2 + • ·.+ an. Prove the following…

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Q: n2n n=1 (1+n)³n converges O diverges

A: It is given that ∑n=1∞ n2n1+n3n. Denote the general term of the series by un.  un=n2n1+n3n. Use…

Q: Which of the followings are true? 1.En 1 nInn (-1)" is absolutely convergent. 11. En 1 (-1) is…

A: Option (e) is correct.

Q: Let an > 0 and assume that an diverges. Write Sn = a1 + a2 + • ·.+ an. Prove the following…

A:

Q: Which of the followings are false? is absolutely convergent. 1. Ln=1 (-1)*-1 is absolutely…

A:

Q: 2. (a) Write the first 5 terms of the sequences with general terms an below and indicate whether…

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Q: What are all of the values of x, such that converges?

A: We have to use GP sum Common Ratio.

Q: diverges. n=1

A:

Q: تفاضل وتكامل )2( نظري 1 If pconverges, then p could be xP to Select one: а. 3/2 stion 1 b. 1 Oc. non…

A: We have to check

Q: the following converge or not

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Q: n=1 n³ cos² n n²e²n + Inn

A:

Q: Which of the followings are true? (-1)" is absolutely conuo

A:

Q: Determine if the geometric series converges or diverges. If a series converges, find its sum. 5 + +…

A: geometric seriesa+ar2+ar3+ar4+ar5+ar6...+arn-1... = ∑1∞arn-1if |r|<1the series converges to…

Q: 22. 2 n-1 T

A:

Q: Which step of the following of the proof of the fact that "if a -→ a, as n 0o, then JaJal" not true?…

A: For 1st the B option is correct .

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.