Question

use Gauss's approach to find the follwoing sums (do not use formulas).
a... 1+2+3+4+...+999
b... 1+3+5+7+...+997

Answer 1

so like
(1+999) +(2 +998) +(3+997)...
and
1+(3+997)+(5+995)+(7+993)...
?

Answer 2

what do i do next?

Answer 3

1+999 =?

Answer 4

you need to realize they are all in groups of 1000

so you count up the number of groups you can make, then add that to whatever number you cant make a group with

Answer 5

i know that they are in a group of 1000..but do i add up 997? im confused?

Answer 6

just focus on the first problem

you can make groups of 1000 up to 501 and 499

999-501 groups of 1000
999-501=498
this leaves 500

so 498 groups of 1000 = 498*1000=498000
add the 500 to it
you get 498500

Answer 7

for the second problem, you need to realize the only number you can't make a group with is 1

then just count up all the groups of 1000 you can make

or you could make groups of 998 but personally 1000 is easier to calculate

Answer 8

249001? is that for the second problem

Answer 9

no idea, didnt calculate it

Answer 10

because you dont have 1 and 999 as a pair
i think there are 248 pairs instead of 249
but im just guessing

Answer 11

thanks