Exercises

Fun Class Activities:

1. Given the recursive definition of the sequence $A(n) = \begin{cases} 2 & \text{if } n = 0 \\ A(n - 1) + 3 & \text{if } n > 0 \end{cases}$
   compute the first 6 terms and derive the closed formula.
2. Given the recursive definition of the sequence $A(n) = \begin{cases} 1 & \text{if } n = 0 \\ 1 & \text{if } n = 1 \\ A(n - 1) + 2A(n - 2) & \text{if } n > 1 \end{cases}$
   compute the terms $A(2), A(3)$, and $A(4)$ of this sequence.
3. Write the recursive definition for $\sum_{i=1}^5 i^2$ (both the base case and the recurrence relation.)
4. Write the recursive definition for $\sum_{i=0}^\infty \frac{1}{3^i}$ (both the base case and the recurrence relation.)