Sum of Powers of Natural Numbers: A Simple Approach by a Mechanical EngineerConvenient formulae for finding the sums of Kth power of first n natural numbers may be useful in some engineering applications. The formulae for k = 1, 2 and 3, are commonly found in the literature. In this ...
The sum of the first n natural numbers is given by \sum_{i=1}^{n}i=\frac{n(n+1)}{2}. Use this fact and mathematical induction to prove that for all n \in \mathbb{N}, \sum_{i=1}^{n}i^3=\left ( \sum_{i=1}^{n}i \right )^2. A ...
Convenient formulae for finding the sums of kth power of the first n natural numbers may be useful in some engineering applications. The formulae for k = 1, 2, and 3, are commonly found in the literature. In this paper, an attempt is made to develop a general algorithm for finding ...
Proof without Words: kth Power of a Natural Number n as the Sum of n Consecutive Odd Numbers (k = 2,3,...)Presents an illustration showing the kth power of a natural number n as the sum of n consecutive odd numbers (k=2,3,...)....