The sum of the r'th roots of first n natural numbers and new formula for factorial

Snehal Shekatkar

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arXiv · 1204.0877

The sum of the r'th roots of first n natural numbers and new formula for factorial

Snehal Shekatkar

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Abstract

Using the simple properties of Riemman integrable functions, Ramanujan's formula for sum of the square roots of first n natural numbers has been generalized to include r'th roots where r is any real number greater than 1.As an application we derive formula that gives factorial of positive integer $n$ similar to Stirling's formula.

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Snehal Shekatkar. 2012-04-04. The sum of the r'th roots of first n natural numbers and new formula for factorial. https://arxiv.org/abs/1204.0877

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