We have sum (n+1)*a_n*x^n, n from 0 to infinity, I need to find the radius of convergence. Using lim(n-> infinity) |a_n/a_(n+1)|=1/|x|, this means that it is convergent from (-inf, -1)and (1, + inf). But I now that the interval of convergence is around 0. Where is my mistake? PLS help, I have exam tomorrow
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If you're using the ratio test, it should be lim n->infinity |a_n+1/a_n| < 1
Then you can factor the |x| and take the limit, and you might get some constant:
c|x| < 1
so tthen |x| < 1/c and 1/c is your radius
The radius of convergence must be proportional from both sides from were the series is centered at, so (-inf, -1) and (1, +infinity) cannot have a radius of convergence when there's a hole in the middle so something is wrong with that answer
Then you can factor the |x| and take the limit, and you might get some constant:
c|x| < 1
so tthen |x| < 1/c and 1/c is your radius
The radius of convergence must be proportional from both sides from were the series is centered at, so (-inf, -1) and (1, +infinity) cannot have a radius of convergence when there's a hole in the middle so something is wrong with that answer