Radius of Convergence for Series: (2n)!/(n!)^2 * x^n

[paulxzt]

Sum of (2n)!/(n!)^2 * x^n with n = 1 to infinity.

So I applied the ratio test..

2(n+1)! * x^n+1 / ((n+1)!)^2 * (n!)^2 / (2n)!*x^n

what does this simplify to? I got it incorrect on an assignment and I believe it is because i made stupid cancellation mistakes..

[2(n+1)] / (n+1) ]] * |x|..

thanks for any help

 

[Unco]

You should arrive at \(\displaystyle \left| \frac{2(2n+1)}{n+1} x \right|\). Perhaps you can spot your error from there - otherwise, show your work.