Find $P _ { k + 1 }$ For the Given $P _ { k }$

Multiple Choice

Find $P _ { k + 1 }$ for the given $P _ { k }$ .
$$P _ { k } = \frac { 4 } { k ( k + 1 ) }$$

A) $P _ { k + 1 } = \frac { 4 } { k ( k + 1 ) } + 1$
B) $P _ { k + 1 } = \frac { 4 } { k ( k + 1 ) } + \frac { 4 } { ( k + 1 ) ( k + 2 ) }$
C) $P _ { k + 1 } = \frac { 4 } { ( k + 1 ) ( k + 2 ) }$
D) $P _ { k + 1 } = \frac { 4 } { k ( k + 2 ) }$
E) $P _ { k + 1 } = \frac { 16 } { ( k + 1 ) ( k + 2 ) }$