I know the answer to these questions, but want to know how.

#1 The 10th term of the expansion of (x-(1/2))^n is -(1001/256)x^5

Find N.

The answer is 14. How do we get this? (I got it through trial and error, but I'm sure there is an easier way...)

#2 Which term in the expansion of ((1/(2x^2)) - x^3)^10 is a constant?

The answer is the 5th term.

I used trial and error for this one too. Though I"m sure there is an easier way too.