Question 1142839: how do you add 1+ 2+ 3+ +4 all the way up to say 200 or 300? Is there an equation to use for that?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Pick a small number for an example that you can see easily:
1+2+3+4+5+6+7+8+9+10 = ??
Group the numbers in pairs, like this:
(1+10)+(2+9)+(3+8)+(4+7)+(5+6)
The sum is now the sum of 5 pairs, with the sum of each pair being 11. So the sum of all the numbers is 5*11 = 55.
It works when the last number is odd also. For example,
1+2+3+4+5+6+7 = (1+7)+(2+6)+(3+5)+4
which gives you 3 1/2 pairs, each with a sum of 8; the sum is 8 times 3 1/2 = 4 times 7 = 28.
In general, if the last number is n, the sum of the first and last numbers is 1+n, and the number of pairs is n/2. That gives you the following general formula for the sum of the integers from 1 to n:
So for your two particular ending numbers,
1+2+3+...+200 = (200/2)(200+1) = 100*201 = 20100
1+2+3+...+300 = (300/2)(300+1) = 150*301 = 45150
Or, for a random odd last number,
1+2+3+...+79 = (79/2)(79+1) = (79/2)(80) = 79*40 = 3160
Answer by ikleyn(52780)  (Show Source):
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