Expert: Bobby Soltani - 9/22/2004

Question
my brother is in the 7th grade and called me with this problem:

what is 1+2+3+4...+500 ?

what is 1+3+5+7...499? (so all the odds)

what is 2+4+6....500? (all evens)

i know there has got to be a simple solution to this and its driving me crazy. if you could help me out i would greatly appreciate it. thanks

Answer
Hi Hester,

The answers are 125,250 62500, and 62750.

Here's how you solve it quickly.

For the first series, the first number plus the last equals 501.  The same for the second number and the second to last number (i.e. 2 and 499).  Therefore you have 250 pairs of numbers that add to 501, so the answer is

250*501 = 125,250

Same for the other two but there are only 125 pairs:

what is 1+3+5+7...499? (so all the odds)
=125*500

what is 2+4+6....500? (all evens)
125*502

I hope this helps you out.  Good Luck.

Bobby