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

Snehal Shekatkar

Published 2012-04-04, updated 2013-02-13Version 2

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.