Find a power series for the function centered at 0.

Name: Find a power series for the function centered at 0.
Brand: Quizplus
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Question

Find a power series for the function  centered at 0. ​

Quizplus · Accepted Answer

We can obtain the power series for the function $f(x)=11\sin(x)$ as follows: 
\begin{align*} 
f(x)&=11\sin(x)\ 
&=11\left(x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+\cdotsight)\ 
&=11\sum_{n=0}^{\infty}\frac{(-1)^nx^{2n+1}}{(2n+1)!}\ 
&=\sum_{n=0}^{\infty}\frac{(-1)^n11^{2n+1}x^{2n+1}}{(2n+1)!}.
\end{align*}
Therefore, the answer is $\boxed{	extbf{(B)}}$.

Find a Power Series for the Function Centered at 0