What is the sum of the whole numbers 1-1000 and how do you get it?
2006-09-17 13:53:47 · 11 answers · asked by tom 2 in Science & Mathematics ➔ Mathematics
500,500
2006-09-17 13:56:00 · answer #1 · answered by MB_Bailey 3 · 1⤊ 1⤋
Note the sum of the series is equal to the sum of the following (divided by 2)
(
(1 + 2 + 3 + 4) +
(4 + 3 + 2 + 1)
)/2
=
(5 + 5 + 5 + 5)/2 = 20/2
So yeah, take average of first and last number and multiply by the number of numbers.
(1 + 1000)/2 = 500.5
#(numbers) = 1000
Answer 500,500
2006-09-17 21:03:09 · answer #2 · answered by Jay 3 · 0⤊ 0⤋
1 + 2 + ... + 999 + 1000 = X
1000 + 999 + ... + 2 + 1 = X
Now sum both lines
(1+1000 ) + ( 2 + 999 ) .... + (999 + 2 ) + ( 1000 + 1 ) = 2 * X
since we have 1000 pairs which add up to 1001 we have
1001 * 1000 = 2 * X
dividing both sides by 2
X = 1001 * 1000 /2
So X = 500500
2006-09-17 21:11:46 · answer #3 · answered by Anonymous · 0⤊ 0⤋
1+2+3+4 = (1+4)/2 * 4 = 10.
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 =
(1 + 10)/2 * 10 = 55
1 + 2 + .... + 99 + 100 =
(1 + 100)/2 * 100 = 5050.
So, what do you think 1 + 2 + ... + 999 + 1000 is?
2006-09-17 20:59:55 · answer #4 · answered by tbolling2 4 · 0⤊ 0⤋
1000(1000+1)/2=500500
2006-09-17 20:56:54 · answer #5 · answered by Jimee77 4 · 2⤊ 0⤋
take the numbers 1000 and 1 and add, which gets 1001. 999 and 2, 998 and 3, and so on all get you 1001. so take how many combos of 1001 you can get and multiply that by 1001-
500 x 1001 = your answer
2006-09-17 20:56:36 · answer #6 · answered by Anonymous · 1⤊ 0⤋
take the average of the 1000 numbers, which would be half way inbetween 1 and 1000 (500) and multiply by 1000 to get 500,000
2006-09-17 20:56:19 · answer #7 · answered by DanE 7 · 0⤊ 1⤋
(1000/2)(1 + 1000) = 500(1001) = 500500
2006-09-18 02:39:50 · answer #8 · answered by Sherman81 6 · 0⤊ 1⤋
500500
1+1000 times half of 1000
2006-09-17 20:55:56 · answer #9 · answered by Ron L 2 · 1⤊ 1⤋
The sum of the first n numbers is 500,500.
Now **you** need to figure out how to do that. (And I did it without a calculator âº)
Doug
2006-09-17 20:56:20 · answer #10 · answered by doug_donaghue 7 · 1⤊ 0⤋
You really need to do your homework on friday not on sunday night!!!
2006-09-17 20:55:25 · answer #11 · answered by Anonymous · 0⤊ 2⤋