Test the following series for convergence.(i) (ii)&

Question

Test the following series for convergence.

(i) $\sum_{n=1}^{\infty}nx^{n-1},x>0.$

(ii) $\sum_{n=1}^{\infty}[\sqrt{n^4+9}-\sqrt{n^4-9}]$

15 Feb 2025

Answer :

Word Count : 271

Let's break down both series and analyze their convergence. ### (i) Series: \[ \sum_{n=1}^{\infty} nx^{n-1}, \quad x > 0 \] This is a power series. To analyze its convergence, we can apply the ratio test or use known convergence properties of geometric series. The general ____ __________ _____ ________ ______ _________ __________ ___ _____ ________ ________ _______.
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