how to you find out that product of 1+2+3+4.....+998+999+1000?

Question

without really adding the numbers one by one?

Answer 1

There's a simple formula by the German mathematician Carl Fredrich Gauss: (n^2 + n)/2, where n is the highest number you are adding up.

There is also a variation of the formula which allows you to add up non-consecutive series of numbers, as long as the numbers have a fixed interval between them.

Answer 2

1000+0=1000 1+999= 1000 2+998=1000 3+997=1000 ....
There are 500 of these combinations. Add 500 (the middle number not already added) to that. And you have 500,500

Answer 3

1+2+ ... +999+1000 =
1+1000 +(2+999) + (3+998) + ... +(500+501) =
1001 + 1001 + ... +1001
500 veces 1001
=500 * 1001
=500500

en general 1+2+...+n = n(n+1)/2

Answer 4

Add the start and end numbers together (1+1000=1001). Counting inwards, all other number pairs are going to add up to 1001 then (2+999, 3+998).

We know that there are 1000/2=500 pairs, so we multiply the 500 by the 1001 and we get...

500500

Alternatively, write a simple computer program to add them all together.

Answer 5

you're talking about the sum, not product.

(1+1000) *1000 /2 gives the answer.

basically you pair up numbers like 1 and 1000, 2 and 999, 3 and 998. They all add up to 1001. there are 500 such pairs.

Answer 6

First of all, you want the sum, not the product.

Second, there's a formula n(n+1)/2.

Third, there's a cheap trick to find the formula, although finding it is part of the legend of the great mathematician Gauss.

(1000+1) + (999 +2) + (998 +3) + ... should be pretty easy to calculate without doing all the hard work. But it's also the sum you're looking for mutliplied by 2.

Answer 7

Hay dear actually this is a series of AP ( since the difference between any two consecutive no is 1.

SO for these type of series (for sum) there is a formula
sum=n(n+1)/2 where n is the value of last term i.e.1000.
Since it has been stated with 1.


So ur answer is 1000(1000+1)/2
= 500*1001
=5005000

Have a nice time!
Bikash Jain

Answer 8

I don't remember where I learned this, but here it is:

0 + 1000 = 1000
1 + 999 = 1000
2 + 998 = 1000
3 + 997 = 1000
and so on until
499 + 501 = 1000

so the answer is
500 x 1000 + 500 = 500,500

Answer 9

Lets call such a sum X
now the sum
1000 + 999 + 998 .... + 2 + 1 =X as well
If we add the two equations we get

1001 + 1001 + 1001 ... + 1001 = 2X

I am willing to bet you can take it from here

Answer 10

Easy way make pairs
1+1000 = 1001
2+999=1001
3+998 = 1001

See the pattern, well there would be 500 pairs, so
500*1001= 500500

Or if you have a good calc that does summations you can.