Question

the sum of the first 1000 counting numbers has a units digit of

Answer 1

\[\Large Welcome~ 2~\Huge\bf \color{#00B4ff}{\bbox[10pt, #7cc517]{Open}}\color{#7cc517}{\bbox[10pt, #00B4ff]{Study}}\]
Do you know any summation formulas (formulas for adding)?

Answer 2

1

it is the sum of 500 pairs of the form

1 + 1000
2 + 999
3 + 998
...
So 500(1001)
and the units must be 1.

Answer 3

thanks

Answer 4

why 1?

isn't it 0? \[\sum_{i=1}^{1000}i = \dfrac{1000(1001)}{2} = 500(1001) = 50050\boxed{0}\]

Answer 5

@LarsEighner

Answer 6

yep he's right