It is known that 11x=n=0xn=1+x+x2+x3+x4+\displaystyle \frac{{1}}{{{1}-{x}}}={\sum_{{{n}={0}}}^{{\infty}}}{x}^{{n}}={1}+{x}+{x}^{{2}}+{x}^{{3}}+{x}^{{4}}+\ldots
on its interval of convergence.

Find a power series for 11+x2\displaystyle \frac{{1}}{{{1}+{x}^{{2}}}}

Write the first 5 terms below, simplifying any powers of -1.

+ + + + + ...
         

Write the series compactly using summation notation (if the series alternates, include the alternator separately):

 n=0\displaystyle {\sum_{{{n}={0}}}^{{\infty}}}   

Find the interval of convergence for the new series.