Which of the followings are false? I. 0 (-1)" is absolutely convergent. Ln=1 n² +Inn 2n II. E (-1) is conditionally convergent. 2" un=1 III. En=1 (-1)"-1 is conditionally convergent. IV. S (-1)"n n+7 is conditionally convergent.

Q: can anything be said about E- an

A: Given that, ∑nan converges.

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

A:

Q: 5. Determine if Σn=3 convergent. cos(NT) is absolutely convergent or conditionally n+1

A: "Absolute convergence" means a series will converge even when you take the absolute value of each…

Q: Rigorously show that (-1)"-1. n2 +1 is conditionally convergent. n=1

A:

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: (1) E(-1)n+1 (3n)! 3n+1 n=1

A: (f). Given series is ∑n=1+∞(-1)n+1(3n)!3n+1

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: Š V2n-5 n=1 n2- 3n +4

A:

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: V2+cos (n2+1) Use the basic comparison test to determine whether E1 n=D1 converges or n+en diverges.

A: To check the Convergency of the given series. We apply here Simple comparison Test and Ratio Test of…

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: 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…

A:

Q: 1 Σ 8n2 – 16n + 6 n=1

A: We will use limit form of comparison test to determine whether given series is convergent or…

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: Which of the followings are true? 2" n1 n! 1. E is absolutely convergent. II. E 1 (-1)"-1 is…

A: see second step

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: 9. Determine whether the following is convergent or divergent +(-1)"+1 n! 2n 2e

A:

Q: diverges. n=1

A:

Q: 2. Which of the following products are absolute convergent? Determine the corresponding values when…

A: To determine if the given infinite products are absolutely convergent, we need to analyze the…