Exercise 4

Find the value of each of the following sums:

1. $\displaystyle \sum_{k=0}^8 3\cdot 2^k$
2. $\displaystyle \sum_{k=1}^8 2^k$
3. $\displaystyle \sum_{k=1}^8 (1 + (-1)^k)$
4. $\displaystyle \sum_{k=1}^8 (2^{k+1} - 2^k)$
5. $\displaystyle \sum_{k=50}^{100} k$