Answer
the intervals of convergence series;
$I=(-1,1)$
Work Step by Step
Given:
$f(x)=\frac{1}{x+1}$
Now we have to write the function in the form of $\frac{1}{1-r}$, then we get the power series as ;
$f(x)=\frac{1}{1+x}$
$=\frac{1}{1-(-x)}$
$=\sum_ {n=0}^ {\infty}(-x)^n$
$=\sum_ {n=0}^ {\infty}(-1)^n(x)^n$
with
$|-x|<1$
$\implies~~|x|<1$, so $R=1$,
Hence, intervals of convergence series;
$I=(-1,1)$
