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Find the interval of convergence. (Give your answer using interval notation.) Sum of (x^n)/(n^5 +...

Question:

Find the interval of convergence. (Give your answer using interval notation.)

{eq}\sum_{n=0}^{\infty} \frac{x^n}{n^5 + 4} {/eq}

Series:

When the given series is in index form, the numerator contains the variable.

Therefore, we will use the ratio test to find the interval of convergence.

Then, we'll find the limits of the expression that contains the consecutive terms of the series.

Answer and Explanation:


The given series is:

{eq}\sum_{n=0}^{\infty} \frac{x^n}{n^5 + 4} \\ {/eq}

If there exists an {eq}N {/eq} so that for all {eq}n\ge N,\:\quad...

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