Ten Foundational Principles for Rapid Summation of Even Consecutive Numbers

Abstract

This research article presents ten pioneering principles introduced by Professor Dr. FazalRehman for rapidly calculating the sums of even consecutive numbers. These principles provide elegant shortcuts that eliminate traditional step-by-step addition and replace it with direct computational formulas based on positional terms. Each principle is supported with ten fully solved examples, demonstrating its universality and effectiveness across small and large even integers. The resulting framework contributes a significant new direction in elementary number theory and computational mathematics by simplifying sequence summations into compact algebraic forms.