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Can you find the closed form expression for this series?

Since Brilliant users are really brilliant, I thought that it would be great to discuss with them my problem. I want to find out a closed form expression for the following series:

\[\sum_{k=1}^{\infty}k^{1-\alpha}\]

Of course this would be function of \(\alpha\). Actually in my case \(\alpha>2\). Any help is greatly appreciated.

Note by Snehal Shekatkar
2 years ago

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Riemann Zeta function for \(\alpha >2\)! *except for that first zero term which as Sudeep Salgia said the value becomes infinity. Kartik Sharma · 2 years ago

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Don't you think that for \( \alpha >2 \) and \(k=0\) the value of the expression becomes infinity. ? Sudeep Salgia · 2 years ago

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@Sudeep Salgia Thanks. That is a typo. Sum starts from \(k=1\). Snehal Shekatkar · 2 years ago

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