Exercise 4.

Consider the sequence \((a_n)_{n \ge 1}\) that starts \(1, 3, 5, 7, 9, \ldots\) (i.e., the odd numbers in order).

1. Give a recursive definition and closed formula for the sequence.

2. Write out the sequence \((b_n)_{n \ge 2}\) of partial sums of \((a_n)\text{.}\) Write down the recursive definition for \((b_n)\) and guess at the closed formula.