**Problem 6**

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.

**Solution**

#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.

n = 100

answer = (n*(n+1) / 2)**2 – (n*(n+1)*(2*n+1)) / 6

puts answer

**Discussion**

And there’s your trick. Incidentally, I need to create a cheat sheet for the math functions in all of these languages. ** is not in my vocabulary. It’s nice though.

If you have questions, leave a comment or please find me on Twitter (@azzlsoft) or email (rich@azzlsoft.com).

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