Posted by Soroban on September 18, 2002 at 13:44:20:
In Reply to: odd even numbers posted by Sachin and Conor on September 18, 2002 at 09:29:08:
: We were trying to figure out what the sum of the first 1000 odd numbers and the first 1000 even numbers, but we kept getting different answers. If someone could help, we would appreciate it!
Do you know the formula for finding the sum of ALL
numbers from 1 to n? It is: n(n + 1)/2
Easily remembered: (last number)x(next number), divided by 2.
So, the sum of ALL number from 1 to 1000 is: 1000(1001)/2 = 500500.
For even numbers: 2 + 4 + 6 + ... + 1000 = 2(1 + 2 + 3 + ... + 500)
Our formula says: 1 + 2 + ... + 500 = 500(501)/2 = 125250
So, the sum of even numbers is: 2(125250) = 250,500.
And the sum of the odd number is what's left over.
[Smugness, arrogance - more free services I offer.]