Problem 2. For each of the following series, determine if it converges and prove your answer.(a)∞∑n=1n44n (b)∞∑n=1n!n4 + 3 (c)∞∑n=12nn!

Question

Problem 2. For each of the following series, determine if it converges and prove your answer.(a)∞∑n=1n44n (b)∞∑n=1n!n4 + 3 (c)∞∑n=12nn!
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Solution 1

(a) ∞∑n=1n/4^n

We can use the ratio test to determine if this series converges. The ratio test states that if the limit as n approaches infinity of the absolute value of the (n+1)th term divided by the nth term is less than 1, then the series converges.

For this series, the (n+1)th term divided by Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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