Giving $a$, $b$ are two positive numbers and $\alpha$ is a positive integer; calculate the limit:$$\lim_{n\to\infty}\left[\dfrac{1}{n^{2\alpha+1}}\sum_{k=1}^{n}\left(k^2+ak+b\right)^{\alpha}\right]$$I think Riemann integral will be useful for this.$$\mbox{But how to make it in the form}\quad\dfrac{1}{n}\sum_{k=1}^{n}\operatorname{f}\left(\dfrac{k}{n}\right)\ ?.$$Please give me a hint.
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