Python/Project Euler/Problem 01/sol2.py

'''
Problem Statement:
If we list all the natural numbers below 10 that are multiples of 3 or 5,
we get 3,5,6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below N.
'''
from __future__ import print_function
try:
    raw_input          # Python 2
except NameError:
    raw_input = input  # Python 3
n = int(raw_input().strip())
sum = 0
terms = (n-1)//3
sum+= ((terms)*(6+(terms-1)*3))//2 #sum of an A.P.
terms = (n-1)//5
sum+= ((terms)*(10+(terms-1)*5))//2
terms = (n-1)//15
sum-= ((terms)*(30+(terms-1)*15))//2
print(sum)