Find the average for the 1000 whole numbers from 1 to 1000, inclusive.
Herllo, aznmartinjai!
Find the average for the 1000 whole numbers from 1 to 1000, inclusive.
Simple . . . add the numbers from 1 t0 1000 and divide by 1000 . . . LOL!
If you know the formula for the sum of the first n positive integers, it's faster.
. . The sum of the first n positive integers is: .n(n + 1)/2
So the sum is: .1000(1001)/2
And the average is: .1000(1001)/2 ÷ 1000 .= .500.5
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If you didn't know that formula, you could still find the sum.
We have: .1 + 2 + 3 + . . . + 998 + 999 + 1000
Add pairs of numbers "from the ends".
. . 1 + 1000 .= .1001
. . .2 + 999 .= .1001
. . .3 + 998 .= .1001
. . . . .and so on . . .
How many such pairs are there?
. . There are five hundred pairs.
Therefore, the sum is: .1001 × 500 .= .500,500