On the summation of certain infinite series and sum of powers of square root of natural numbers

Ramesh Kumar Muthumalai
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 20, 2014, Number 3, Pages 36–44
Full paper (PDF, 177 Kb)

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Authors and affiliations

Ramesh Kumar Muthumalai
Department of Mathematics, D.G. Vaishnav College, Arumbakkam
Chennai-600106, Tamil Nadu, India

Abstract

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.

Keywords

• Hurwitz zeta function
• Riemann zeta function
• Infinite series
• Ramanujan notebooks

AMS Classification

• 11M06
• 11M35
• 40A05

References

1. Berndt, B. C., Ramanujan Notebooks, Part V, Springer–Verlag, New York, 1998.
2. Gradshteyn, I. S., I. M. Ryzhik, Tables of Integrals, Series and Products, 6 Ed., Academic Press, USA, 2000.
3. Ramanujan, S., Summation of certain series, Mess. Math., Vol. XLIV, 1915, 157–160.
4. Ramanujan, S., On the sum of the square roots of the first n natural numbers, Jour. Indian Math. Soc., Vol. VII, 1915, 173–175.