I would use the ratio test on the sum of n = 1 to infinity, the algebra is easier. Clearly this should be greater than the sum of n = p+1 to infinity, so if it converges for the larger series, the smaller series must converge too.
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??