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edit approved Jan 10 at 19:41
J. W. Tanner
edit approved Jan 10 at 19:41
J. W. Tanner
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Capitalise title; `\Sigma` -> `\sum`
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LSpice
LSpice
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binomial Binomial series

I am interested in the limit $\frac{\Sigma_{k=0}^n \sqrt{k}.\binom{n}{k}}{\sqrt{n}.2^n}$$\frac{\sum_{k=0}^n \sqrt{k}\cdot\binom{n}{k}}{\sqrt{n}\cdot2^n}$ as $n$ goes to infinity. Any reference or argument?

In general what do we know about the asymptotic behavior of $\Sigma_{k=0}^n k^\alpha.\binom{n}{k}$$\sum_{k=0}^n k^\alpha\cdot\binom{n}{k}$, where $\alpha$ is a positive real (not necessarily integer)?

binomial series

I am interested in the limit $\frac{\Sigma_{k=0}^n \sqrt{k}.\binom{n}{k}}{\sqrt{n}.2^n}$ as $n$ goes to infinity. Any reference or argument?

In general what do we know about the asymptotic behavior of $\Sigma_{k=0}^n k^\alpha.\binom{n}{k}$, where $\alpha$ is a positive real (not necessarily integer)?

Binomial series

I am interested in the limit $\frac{\sum_{k=0}^n \sqrt{k}\cdot\binom{n}{k}}{\sqrt{n}\cdot2^n}$ as $n$ goes to infinity. Any reference or argument?

In general what do we know about the asymptotic behavior of $\sum_{k=0}^n k^\alpha\cdot\binom{n}{k}$, where $\alpha$ is a positive real (not necessarily integer)?

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Morteza
Morteza
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binomial series

I am interested in the limit $\frac{\Sigma_{k=0}^n \sqrt{k}.\binom{n}{k}}{\sqrt{n}.2^n}$ as $n$ goes to infinity. Any reference or argument?

In general what do we know about the asymptotic behavior of $\Sigma_{k=0}^n k^\alpha.\binom{n}{k}$, where $\alpha$ is a positive real (not necessarily integer)?