How can I solve this limit?
thanks you!!!
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1$\begingroup$ How is it related to Mathematica programming? $\endgroup$– ArtesCommented Oct 12, 2015 at 11:02
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1$\begingroup$ This is not a site for homework problems that show no coding attempt. There may be related sites for that, I'm not sure. $\endgroup$– Daniel LichtblauCommented Oct 12, 2015 at 15:49
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$\begingroup$ 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/… $\endgroup$– Dr. Wolfgang HintzeCommented Oct 13, 2015 at 8:55
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1 Answer
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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
