Example 2.1.5.

Sam keeps track of how many push-ups she does each day of her “do lots of push-ups challenge.” Let \((a_n)_{n \ge 1}\) be the sequence that describes the number of push-ups done on the \(n\)th day of the challenge. The sequence starts

\begin{equation*} 3, 5, 6, 10, 9, 0, 12, \ldots\text{.} \end{equation*}

Describe a sequence \((b_n)_{n \ge 1}\) that describes the total number of push-ups done by Sam after the \(n\)th day.

Solution.
in-context