Find the Sum of the Series $$\sum _ { i = 1 } ^ { 5 } \frac { ( \mathrm { i } + 2 ) ! } { ( \mathrm { i } + 1 ) ! }$$

Multiple Choice

Find the sum of the series.
- $$\sum _ { i = 1 } ^ { 5 } \frac { ( \mathrm { i } + 2 ) ! } { ( \mathrm { i } + 1 ) ! }$$

A) 19
B) $\frac { 129 } { 20 }$
C) 25
D) $\frac { 377 } { 60 }$