# What is the interval of convergence of #sum_1^oo [x^(2n+1)]/[(2n+1)!]#?

The interval of convergence is

We employ the test of ratios.

We now determine the limits.

Consequently,

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The interval of convergence for the series (\sum_{n=1}^{\infty} \frac{x^{2n+1}}{(2n+1)!}) is ((- \infty, \infty)).

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