Find a power series rep for the function and determine the interval of convergence:
$$f(x)= \frac{1}{x+10}$$
$$f(x)=\frac{1}{10}*\frac{1}{1-(-\frac{x}{10})}$$
$$\sum_{n=1}^{\infty} \frac{1}{10} (-\frac{x}{10})^n$$
$$\sum_{n=1}^{\infty} \frac{1}{10} (-1)^n\frac{x^n}{10^n}$$
$$r=\frac{x}{10}$$
$$|\frac{x}{10}|

Question

Find a power series rep for the function and determine the interval of convergence:
$$f(x)= \frac{1}{x+10}$$
$$f(x)=\frac{1}{10}*\frac{1}{1-(-\frac{x}{10})}$$
$$\sum_{n=1}^{\infty} \frac{1}{10} (-\frac{x}{10})^n$$
$$\sum_{n=1}^{\infty} \frac{1}{10} (-1)^n\frac{x^n}{10^n}$$
$$r=\frac{x}{10}$$
$$|\frac{x}{10}|<1$$
$$-10<x<10$$
R=10
I believe this is correct

turingtest · Answer

and again, I believe you are right :)

anonymous · Answer

Good. Thanks!