Which of the following statement is TRUE? (i) If Σα o an = and bn = then Στο bn n=0 2 an 3 (ii) If an is convergent series with positive terms, then sec(an) converges +∞ in=0 in=0 (iii) If an > 0 and Σ₁ an diverges, then the series ₁ (an)² also diverges. n=1 n=1 (i) and (ii) only All of the above are true None of the above are true (i) and (iii) only O (iii) only =

Q: 2 (a) Use the Comparison Test to show that the series En-1 4n3n²+3 converges. (You may use the fact…

A: We have to check the convergence of the following series.

Q: Let an (2n³ + 1) sinn n² +1 (1) Does the sequence (2) Does the series n=1 n² + 1 (2n³ + 1) sinn n¹ +…

A: Here we have given a sequence  where,

Q: n³+2n²+3n-5 Does the series Σ=1 n6+3 converge or diverge? By what test?

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Q: (c) One of these series converges absolutely. Which one? Compute its sum.

A:

Q: 6) Which of the following series diverge? 1. Σ/sin2 71-0 TT II. 00 Στη e" III. (1) e" +1 n=1 (A) III…

A: ∑n=0∞sin2πn ∑n=1∞1n3 ∑n=1∞enen+1 We have to find which of the following series is divergent

Q: (a) Give an instance of the Binomial Series which begins as follows: 10 1 - 6z² +24z¹ - 80z6 +240z8…

A: Given binomial series Note: According to the guidelines we are allowed to solve one question at a…