Use a power series to approximate the definite integral,

17

Use a power series to approximate the definite integral, $$I$$, to six decimal places.

$$\int_{0}^{0.4} \frac{x^{5}}{1+x^{7}} d x$$

Find the radius of convergence, $$R$$, of the series.

$$\sum_{n=1}^{\infty} \frac{x^{n+4}}{4 n !}$$

$$R=$$

Find the interval, $$I$$, of convergence of the series. (Enter your answer using interval notation.) $$I=$$

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