Sage doesn't show limit of ratio of sums

edit

Hi everyone,

I'm new to Sage and I'm trying to obtain the following limit: $$\lim_{N\to \infty}\frac{\sum_{i=1}^{N} x_i^{5/2}}{\sum_{i=1}^N x_i^2}$$ with $x_i=(N-i)/(N-1)$. What I tried was:

i = var('i')
assume(i>0,'integer')
N = var('N')
assume(N>0,'integer')
x_i = (N-i)/(N-1)
numerator = sum(x_i^(5./2.),i,1,N)
denominator = sum(x_i^(2.),i,1,N)
limit(numerator/denominator,N=oo)

However, this just gives me:

6*limit((N - 1)*sum(((N - i)/(N - 1))^2.5, i, 1, N)/(2*N^2 - N), N, +Infinity)

From what I can see, Sage has no problems with the denominator, the general formula of which was obtained easily. However, apparently it has problems obtaining the general formula for the numerator due to the fact that the exponent in the sum is not an integer. Is there a way to cope with this? How can I obtain the limit?

Thanks in advance for all the help!