SOLUTION: Calculate the sum of all even positive integers from 2 to 4000.

Question 38187: Calculate the sum of all even positive integers from 2 to 4000.
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Gauss showed the shortcut for this hundreds of years ago, when he was but a child...
Notice that if you add the first and last terms you get 4002.
If you add the second and second-to-last terms you get 4002.
If you add the third and third-to-last terms you get 4002.
And so on, and so on...
Now how many pairs making 4002's are there?
Well, half the number of numbers present.
There are 2000 even numbers from 2 to 4000.
That means 1000 pairs, each adding to 4002.
So the sum is 1000 * 4002 = 4002000.
Cool!
RELATED QUESTIONS
Find the sum of all positive even integers from 1-100 (answered by Alan3354,MathLover1)

Find the sum of all even five-digit positive integers that are multiple of... (answered by Edwin McCravy)

Consider the integers from 1 to 100 inclusive. What is the difference between the sum of... (answered by nabla)

Find the sum of the first 100 even positive... (answered by rfadrogane)

the sum of the positive even integers less than... (answered by rfer)

Find the sum of the first 100 positive even integers. 2+4+6+8+....+200 (answered by josgarithmetic)

The sum of the positive odd integers less than 100 is subtracted from the sum of the... (answered by vleith)

The sum of the positive odd integers less than 50 is subtracted from the sum of the... (answered by Fombitz)

What is the difference between the sum of all postive odd integers less than 102 and the... (answered by Alan3354,Edwin McCravy)