Thread: power series problem.

looks like this: f(x) = x/(9+x^2)

need to find the interval of convergence.

thanks for any help.

Originally Posted by rcmango

looks like this: f(x) = x/(9+x^2)

need to find the interval of convergence.

thanks for any help.

f(x) = x/(9+x^2) = x/9 [1+(x/3)^2]

and the usual series expansion of 1/(1+(x/3)^2) is derived from that of
1/(1+z), with z=(x/3)^2, which is convergent for |z|<1, so is convergent for
|x|<3.

RonL