what is the sum of the remainders if the numbers 100, 101, 102...998, 999,1000 are divided by nine?

Question

i need help and i need it FAST. I don't want the answer, but just how i might get to it with some sort of short cut.

Answer 1

all integers from 102 thru 1000

divide bi 9 & add the leftovers

yu hav 899 numbers

thats 99.9 sets av 9 numbers

eech set av 10 numbers hav leftover=0, 1, 2, 3, 4, 5, 6, 7, 8

1 set sum=36

100 sets=3600

then chek a fyu numbes at both ends

102/9=11 with leftover=3

1000/9=111 with leftover=1

lak leftover=2, su anser=3600-2=3598

Answer 2

What is 100+101+...999?