A study on power summation of positive integers

The main objective of this article is to discuss the literature on the sum of powers of integers and propose some generalized results with interesting numerical examples. This power sum is evaluated with one recurrence relation based on ar eas of rectangles. We have described the proof of the recurrence relation with the universal rectangle and its interior rectangles. In this paper Pascal’s generalized result is given from which power sum for any fixed positive integer can be derived. Illustrat ive examples in Pascal’s formula will clear the methods of computing the sums namely sum of first n-natural numbers, sum of squares of first n-natural numbers, sum of cubes of first n-natural numbers and so on. We have given a powerful formula for power sum using Bernoulli’s coefficients. First ten Bernoulli’s coefficients are calculated and are used in extracting first ten power sums.