Question

5. Complete the following two problems.\\ a) Prove $\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^2}$ converges;\\b) Assume that $\sum_{n=1}^{\infty} |a_n|$ converges. Prove $\sum_{n=2}^{\infty} \frac{\sqrt{|a_n|}}{\sqrt{n} \ln n}$ converges.

          5. Complete the following two problems.\\
a) Prove $\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^2}$ converges;\\b) Assume that $\sum_{n=1}^{\infty} |a_n|$ converges. Prove $\sum_{n=2}^{\infty} \frac{\sqrt{|a_n|}}{\sqrt{n} \ln n}$ converges.

5. Complete the following two problems.

a) Prove ∑n=2^∞(1)/(n(ln n)^2) converges;
b) Assume that ∑n=1^∞ |an| converges. Prove ∑n=2^∞(√(|an|))/(√(n)ln n) converges.

Added by Miriam B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/27/2023

Step 1

To determine whether the series converges or diverges, we can use the integral test. The integral test states that if f(x) is a positive, continuous, and decreasing function for x ≥ N, where N is a positive integer, and if the series Σf(n) converges or diverges, Show more…

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