(n^2-n)+((n-1)^2-(n-1))+....+(1^2-1) =n(n+1)(2n+1)/6 - n(n+1)/2

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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I cannot understand the followings.

(n^2-n)+((n-1)^2-(n-1))+....+(1^2-1)

=n(n+1)(2n+1)/6 - n(n+1)/2

Expert Solution
Step 1

We shall first derive the formulas for sum of first n natural numbers and sum of squares of first n natural numbers and those formulas will help us to solve the given problem. Follow the next steps for the solution.

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