Ramesh Kumar Muthumalai

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 20, 2014, Number 3, Pages 36—44

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## Details

### 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

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

## Related papers

## Cite this paper

APAMuthumalai, 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.

ChicagoMuthumalai, Rafael. “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, no. 3 (2014): 36-44.

MLAMuthumalai, Rafael. “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 (2014): 36-44. Print.