# 1+2+3+4...1000?

Question:I was working in a primary school the other day and i saw the question: "if I add 1+2+3+4 all the way to +1000 what is the answer?" Was this a crucial part of primary I missed?! How do you figure this out?

500,500. It was Karl Gauss's summation formula. n = 1,000 (in this case).

(n/2)*(n+1)= 500 * 1,001 = 500,500.
Why dont you just add them up X Cindy
You figure it out by adding them up, makes the kids think about BIG numbers
You know a bit like the chess board question, put one grain of rice on the first square, 2 on the second, 4 on the third, keep doubling the no. of grains of rice on each square, how many grains go on the last square ?
The formula for that equation as I remember is:
(n/2)*(n+1). N is equivalent to your last number.
If you add up every consecutive number from 1 (one) to 1000 (one thousand) you get a total of 500,500 (five hundred thousand five hundred).
500,500

If the you don't like using the formulas think of it like this...
imagine pairing the numbers up 1000+1, 999+2, you can do this until you get to 501+500, so you end up with 500 x 1001=500,500
500,500
500,500
Let x = 1 + 2 + .. + 1000
Writing the numbers backwards underneath:
x = 1000 + 999 + 998 + ... + 1
(On paper you will be able to line them up vertically in pairs.)
Each vertical pair adds up to 1001.
Therefore when you add these two equations, you get:
2x = 1001 + 1001 + 1001 + . + 1001
There are 1000 terms in the series, and therefore:
2x = 1001 * 1000
Dividing by 2:
x = 1001 * 1000 / 2
= 1001000 / 2
= 500500. 