Find, as function of , the sum of the infinite series and state its interval of convergence.
Hey, I hope this is the right board..
How would I determine the answer? I think it's a combination of power series, (like + another series or something like that) but I'm just guessing.
Thanks.
Hello,
You're looking for :
Factor out x :
And you can see that this simplifies to :
Provided that , this is a convergent geometric series (multiplied by x)
Edit : muff...too late ><
Editē :
Well, actually you have to state the condition over x before writing what f(x) isSo this is a geometric series with r=(-2x) so we get
f(x)=x\cdot \frac{1}{1+2x}=\frac{x}{1+2x}
Remember that geometric series converege when r< 1