Exercise 3.9
Consider the recurrence relation $a_n = 8a_{n-1} - 16a_{n-2}$. Are the following valid solutions to
this recurrence relation? If so, compute $a_0, a_1, \dots, a_4$ using the formula.
1. $(a_n) = 0$
2. $(a_n) = n4^n$
3. $(a_n) = n^2 4^n$
4. $(a_n) = (2 + 3n)(4^n)$
Exercise 3.10
Determine the sum of the following summations.
1. $\sum_{i=0}^{10} i + 3$
2. $\sum_{i=0}^{20} 2i + 5$
3. $\sum_{i=0}^{20} (a_i)$ where $a_i = a_{i-1} + 10$ and $a_0 = 0$