CPM Homework Help : APCALC Problem 10-16

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:

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?

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

Hint:

If $n = 1$ , how can you write expressions for $2$ and $3$ ?

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

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