# How can I solve this limit? [closed]

How can I solve this limit?

thanks you!!!

• How is it related to Mathematica programming? – Artes Oct 12 '15 at 11:02
• This is not a site for homework problems that show no coding attempt. There may be related sites for that, I'm not sure. – Daniel Lichtblau Oct 12 '15 at 15:49
• As the sum in the denominator is simply n^(5/2) the expression in question is just the Riemann sum the limit of which gives Integrate[x^(3/2),{x,0,1}] -> 2/5. The same idea was applied in my question mathematica.stackexchange.com/questions/95126/… – Dr. Wolfgang Hintze Oct 13 '15 at 8:55

You can easily look up manual, and employ

Limit[Sum[k*Sqrt[k], {k, 1, n}]/(Sqrt[n]*Sum[2*k - 1, {k, 1, n}]),
n -> Infinity]

(* 2/5 *)


Also track the dependence of the limit on parameter (u) using

ListPlot[Table[{u,
Limit[Sum[k*Sqrt[k], {k, 1, n}]/(Sqrt[n]*Sum[u*k - 1, {k, 1, n}]),
n -> Infinity]}, {u, 1, 4, 0.1}]]


The arrow indicates value corresponding to u=2