I am trying to find the series' radius and interval of convergence and for what values of x the series converge b) absolutely, c) conditionally?
1) n = 1 to infinite, n^r*x^n, r real.
2) n = 1 to infinite, (3^n(x-1)^n)/n^3
3) n = 1 to infinite, ((n!)^2 * x^n)/(2n)!
So I know I need to apply the ratio test, and that left me with ((n+1)^r*x)/n^r for the first one, (3(x-1)*n^3)/(n+1)^3 for the second, and ((n+1)^2*x)/2(n+1) for the third-- assuming I did this correctly. I just don't understand what to do next. Any help would be very appreciated!