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Summation of certain infinite series involving powers of square root of natural numbers is evaluated through Riemann zeta function. The sum of powers of square root of first n natural numbers are expressed in terms of infinite series and Riemann zeta function.
- Hurwitz zeta function
- Riemann zeta function
- Infinite series
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- Ramanujan, S., On the sum of the square roots of the first n natural numbers, Jour. Indian Math. Soc., Vol. VII, 1915, 173–175.
Cite this paper
Muthumalai, R. K. (2014). On the summation of certain infinite series and sum of powers of square root of natural numbers. Notes on Number Theory and Discrete Mathematics, 20(3), 36-44.