Question

Help how can I add all the numbers from 1 to 100 without actually adding all of them one by one?!

Answer 1

sure

Answer 2

by "all the numbers" you mean all the whole numbers right?
\[1+2+3+...+98+99+100\]

Answer 3

yup

Answer 4

there is a nice formula for this but we can see how it works by adding forwards and also backward

Answer 5

\[1+2+3+...+98+99+100\]
\[100+99+98+...+3+2+1\]

Answer 6

you see that you will add to get
\[101\] in each spot.

Answer 7

what how does that help?

Answer 8

oh you're right

Answer 9

so that means there's a hundred '101s'

Answer 10

THEN IT MUST BE 10100!

Answer 11

exactly!

Answer 12

oops

Answer 13

thanks!

Answer 14

not 10100 because that is both of them together

Answer 15

oh yea, so i have to divdie that by 2

Answer 16

2 times your sum is 10100 so your sum is half of that

Answer 17

got it

Answer 18

THANKS satellite73! you made it very clear!

Answer 19

general formula is
\[1+2+3+...+n=\frac{n(n+1)}{2}\]

Answer 20

yw