How can you add all the numbers from 1 to 999 with Gauss-Seidel method and what is the answer?

Question

How can you add all the numbers from 1 to 999 with Gauss-Seidel method and what is the answer?

Answer 1

not sure what the Gauss- Seidel method is

But you can take 1+999=1000 + 2+998=1000 ....etc

all the way to 499+501=1000

Thus you now have 499 x 1000= 499000 + the 500 that wasnt added yet. Resulting in

499500

Answer 2

recognize that:

1+999=1000

2+998=1000

3+997=1000

this process will allow you to add all integers as part of a pair, except for the number 500 which has no pair

there are 499 such pairs that sum to 1000 plus 500, so the sum is 499,500

Answer 3

(first +last)*entries/2

1000*999/2 = 499,500