# 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
3 years, 5 months 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.

- 3 years, 5 months ago

Don't you think that for $$\alpha >2$$ and $$k=0$$ the value of the expression becomes infinity. ?

- 3 years, 5 months ago

Thanks. That is a typo. Sum starts from $$k=1$$.

- 3 years, 5 months ago