I was told to show that if 0<r<1 and p is any positive integer, sum of n = p+1 to infinity n(n-1)...(n-p)r^n is convergent using ratio test.

when I get Vn+1/Vn I got (n+1)/(n-p)r^n which tells me the series is divergent as it goes to infinity??? can you help me out???

and also can you help to figure this out using the root test??

Thanks