# Project Euler | Problem 6 | Sum square difference

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__Problem Description__ :

The sum of the squares of the first ten natural numbers is, 1^2 + 2^2 + ... + 10^2 = 385. The square of the sum of the first ten natural numbers is, (1 + 2 + ... + 10)^2 = 55^2 = 3025. Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 − 385 = 2640. Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum?

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__Concept__ :

This is a very simple problem. We have to apply following two properties to solve this problem mathematically.

- Sum of first N natural numbers is N(N+1)/2.
- Sum of square of first N natural numbers is N(N+1)(2N+1)/6

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__Java Program__ :

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__Output__ :

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__References__ :

http://www.9math.com/book/sum-first-n-natural-numbers

http://www.9math.com/book/sum-squares-first-n-natural-numbers

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**Tags : Project Euler Problem 6 solution in Java, Sum square difference, Mathematics problems, Sum of first n natural number, sum of square of first n natural numbers.**

Project Euler | Problem 6 | Sum square difference
Reviewed by Rohit Agarwal
on
1/11/2017
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