A review of literature on power sum of natural numbers

This paper explores on deriving the formulae for fixed power sum of natural numbers. A review of literature on power sum is presented in a lucid manner. Here a general method is depicted by applying some results in differential calculus. Moreover, an important application of Pascal’s triangle in computing this sum is discussed. Finding the generalized formula for the power sum has been a fascinating problem for centuries in the research world of Analytical Number Theory. Following discussion presents number of interesting results on this sum with illustrative examples. At first, we gave the early history of the power sum and then move to the various methods of finding this sum. We have proposed a double series formula to the power sum from which the power sums upto 10th order is calculated.