sum_(n=0)^oo (-1)^nx^n Find all values of x for which the series converges. For these values of x write the sum of the series as a function of x.

sum_(n=0)^oo(-1)^nx^n 
=sum_(n=0)^oo(-1x)^n
It is a geometric series with common ratior=-x ,so the series converges for |r|<1  
|-x|<1
=>|x|<1
=>-1In this case, Sum of the series=a/(1-r)
=1/(1-(-x))
=1/(1+x)