I wish to comment more on my observations with nodejs var sum = 0 for ( var i = 0 ; i < 100000000 ; i++) { sum +=i //this is slower. Use sum = sum + 1 //sum += 1 gave me 1.963235s on my machine whereas //sum = sum + 1 gave me 0.506995s } console .log(sum); //I also rewrote it using while loop and the performance increase var sum = 0 ; limit = 100000000 ; while (limit > 0 ) { sum = sum + limit--; } console .log(sum) //I noticed the summation was completed in 0.214555s //The ram of my system is 6GB, core i3.

print(sum(xrange(100000000))) gives 4999999950000000 while print(sum(xrange(100000001))) gives 5000000050000000 Then it is safe to conclude that the first one is actually from 1 to 99999999 and 100000001 is 1 to 100000000