Exercise 14.

Expand the following sums and products. That is, write them out the long way.

1. \(\d\sum_{k=1}^{100} (3+4k)\text{.}\)

2. \(\d\sum_{k=0}^n 2^k\text{.}\)

3. \(\d\sum_{k=2}^{50}\frac{1}{(k^2 - 1)}\text{.}\)

4. \(\d\prod_{k=2}^{100}\frac{k^2}{(k^2-1)}\text{.}\)

5. \(\d\prod_{k=0}^n (2+3k)\text{.}\)