Telescoping Series/Example 2

Theorem
Let $\left \langle {b_n} \right \rangle$ be a sequence in $\R$.

Let $\left \langle {a_n} \right \rangle$ be a sequence whose terms are defined as:
 * $a_k = b_k - b_{k - 1}$

Then:
 * $\displaystyle \sum_{k \mathop = m}^n a_k = b_n - b_{m - 1}$