Posted by Paul on Wednesday, December 1, 2010 at 6:52pm.
So you want the sum of 1+2+3+....+12+13+14.
Well, there are 14 numbers. Divide them in half at 7, divide them again at 3 1/2 and 10 1/2
so 1/4 of the numbers are closest to zero, 1/2 of the numbers are closest to 7, and 1/4 of the numbers are closest to 14
Sum= 1/4*14*1+1/2*14*7+ 1/4*14*14
= 3.5+49+49=102 about
This is not 3rd grade, I had this method in highschool.
Now here is another method, a college method, call the sum of arithemetic series..
Sum= 14/2 *(1+14)=7*15=105
So the estimate was not far off.
form
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