Find the limit for Sum[n^p,{n,1,n0}]/n0^{p+1} when n0 goes to infinity
My way of doing this is to first assume that the limit does exist and the value is c.
Then when n0 is big enough, Sum[n^p, {n,1,n0}]/n0^{p+1} = c is a very good approximation. Thus,
Sum[n^p,{n,1,n0}]=c n0^{p+1} (*)
For the same reason,
Sum[n^p{n,1,n0+1}=c (n0+1)^{p+1} (**)
From equation (*) and (**), you can solve that c=1/(p+1).//Done
