rocedwrp

2021-03-06

Find the interval of convergence of the power series.

$\sum _{n=0}^{\mathrm{\infty}}\frac{{x}^{5n}}{n!}$

avortarF

Skilled2021-03-07Added 113 answers

Consider the given power series:

Here the objective is to find the interval of x for which the given power series is convergent.

According to the ratio test

If

If

Here

Use ratio test for convergence

Substitute

Here the limit is less than 1, and independent of the value of x.

Hence the given power series is convergent for all

Jeffrey Jordon

Expert2021-12-27Added 2605 answers

Answer is given below (on video)

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