2.14 and 2.34 are similar; consider the Binomial Theorem, and how you can prove $$\binom{n}{0} + \binom{n}{2} + \binom{n}{4} + \cdots = 2^{n-1},$$ and do something similar.

For 2.32, you may combine these two sums into one complex number: the first sum is the real part and the second sum is the imaginary part.