Problem Description

The sum of the squares of the first ten natural numbers is,

The square of the sum of the first ten natural numbers is,

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.

Analysis

The formula for finding the square of the sum is adapted from Problem 1: (n*(n+1)/2)**2. The formula for finding the sum of the squares is: n * (n+1) * (2*n+1) / 6. We use these formulas and find the difference between the sum of the squares and the square of the sum.

Solution

Runs < 1 second in Python.

n = 100;
sqofsum = (n*(n+1) / 2) ** 2
sumofsq = n * (n+1) * (2*n+1) / 6
print "Answer to PE6 = ",sqofsum - sumofsq

Comments