I don't understand this please who understand ?
I have read somewhere that: As $j$ tends to $\infty$, $\displaystyle\sum_{j=0}^{n-1} j^{a}$ is asymptotic to $cn^{a+2}$ if $a>-1$, is asymptotic to $cn\ln n$ if $a=-1$, and asymptotic to $n$ if $a<-1$.Perhaps it is as $n$ tends to $\infty$