Find $f(n)$ such that $\sum_{k=1}^{n} k^{1.23}\sim f(n)$

by Gaha   Last Updated September 14, 2018 15:20 PM

Find $f(n)$ such that $\sum_{k=1}^{n} k^{1.23}\sim f(n)$.

I tried to use generating functions. To proceed I need to calculate $\sum_{n\geq0} n^{1.23}x^{n}$ (or something asymptotically similar, because I don't need the exact solution). I know how to do $\sum_{n\geq0} nx^{n}$ or $\sum_{n\geq0} n^{2}x^{n}$, but not anything in between. So after all I guess this method won't work here.

I would appreciate any tips!

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