CPM Homework Help : CALC Problem 10-8

Rewrite the series $S = \frac { 1 } { 2 \cdot 3 } + \frac { 1 } { 3 \cdot 4 } + \frac { 1 } { 4 \cdot 5 } + \ldots$ three different ways using sigma notation by completing the following expressions:

$S=\displaystyle\sum _ { n = 1 } ^ { \infty } ( \space{ \ \ \ \ \ \ })$

$S=\displaystyle\sum _ { n = 0 } ^ { \infty } ( \space{ \ \ \ \ \ \ })$

$S=\displaystyle\sum _ { n = 5 } ^ { \infty } ( \space{ \ \ \ \ \ \ })$

Hint:

Your expression will be a fraction with $1$ in the numerator and the expression for the pattern in the denominator. What is the pattern in the denominator?
If $n = 1$ , how can you write expressions for $2$ and $3$ ?