Question

Find the radius and interval of convergence of E n=1 to infinity, of sqr(n)(x^n)

Answer 1

try ratio test see if it works

Answer 2

I dont know the steps..

Answer 3

lim abs[ a(n+1) / a(n) ]
n-> inf

and we want the limit to be less than 1

Answer 4

Hmmm okay but what about the problem? Why did you change it?

Answer 5

lim abs [ sqrt(n+1) x^(n+1) / (sqrt(n) x^n) ]
n->inf

Answer 6

\[\sum_{n=1}^\infty\sqrt n~x^n~~?\]

Answer 7

I agree with using the ratio test. Figure out the limit:
\[\lim_{n\to\infty}\left|\frac{\sqrt{n+1}~x^{n+1}}{\sqrt n~x^n}\right|=L\]
The series converges if the limit \(L<1\).