Question

8. [10 points total] Use power series to evaluate the following integral. Write your answer in sigma notation and simplify. \[ \begin{array}{l} \int \frac{1}{1+x^{7}} d x=\int \frac{1}{1-(-x)^{7}} d x \\ \rightarrow \sum_{n=0}^{\infty}\left\{(-x)^{7}\right\}^{n}=\left|\sum_{n=0}^{\infty}(-1)^{7 n}(x)^{7 n}\right| \\ |x|<1 \quad R=1 \mid \end{array} \]

          8. [10 points total] Use power series to evaluate the following integral. Write your answer in sigma notation and simplify.
\[
\begin{array}{l} 
\int \frac{1}{1+x^{7}} d x=\int \frac{1}{1-(-x)^{7}} d x \\
\rightarrow \sum_{n=0}^{\infty}\left\{(-x)^{7}\right\}^{n}=\left|\sum_{n=0}^{\infty}(-1)^{7 n}(x)^{7 n}\right| \\
|x|<1 \quad R=1 \mid
\end{array}
\]

$8. [10 points total] Use power series to evaluate the following integral. Write your answer in sigma notation and simplify. ∫(1)/(1+x^7) d x=∫(1)/(1-(-x)^7) d x →∑n=0^∞{(-x)^7}^n=|∑n=0^∞(-1)^7 n(x)^7 n| |x|<1 R=1 |$

Added by Tammy J.

Calculus: Early Transcendentals

James Stewart 8th Edition

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8. [10 points total] Use power series to evaluate the following integral. Write your answer in sigma notation and simplify. \[ \begin{array}{l} \int \frac{1}{1+x^{7}} d x=\int \frac{1}{1-(-x)^{7}} d x \\ \rightarrow \sum_{n=0}^{\infty}\left\{(-x)^{7}\right\}^{n}=\left|\sum_{n=0}^{\infty}(-1)^{7 n}(x)^{7 n}\right| \\ |x|<1 \quad R=1 \mid \end{array} \]