How do i simplify this in terms of n?
Try using the partial sum for a geometric series formula.
r is the common ratio and a is the first term.
So, from the first one we have
The second one is the same only multiplied by n. Giving
The third only can be found by differentiating the partial sum formula.
Sub in x=2 and we get .
Don't forget to divide by 2 because of the 1/2.
Add this with the other two sums and we get:
Just one way to go about it. Remember, you can play around with the geometric series formulas by differentiating, integrating, and so on, and get away with a lot.