After some algebra, I found the whole expression equal to 10^9(1+ 2*(11/10) +3*(11/10)^2+...+10(11/10)^9)
The expression in inside the bracket is similar to power series of (1-x)^2. But, I don't know how to get a finite sum of n terms of (1-x)^2 series.
Need a hint. (Just need a hint, I know it's too easy)