Question

what is the sum of the intergers from 1 to 50?

Answer 1

hmmm.....

(50+1) + (49+2) + (48+3) + ... + (2+49) + (1+50)
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2

Answer 2

or:

51 done 50 times; and divide by 2

Answer 3

it might be easier to see with the number 1 thru 6

(1+6) + (2+5) + (3+4) + (4+3) + (5+2) + (6+1) ; as you can see; there are parts that are counted twice; so we just have to account for that.

7(6) = 42; but thats twice as much as we want.

42/2 = 21 is the true count