Consider a sequence of numbers $a_1, a_2, a_3, \dots , a_n$ where $a_n = \dfrac{1}{n}-\dfrac{1}{n+2}$, for each integer $n>0$. Whart is the sum of the first $50$ terms?

1. $\bigg( 1+ \dfrac{1}{2} \bigg) - \dfrac{1}{50} \\$
2. $\bigg( 1+ \dfrac{1}{2} \bigg) + \dfrac{1}{50} \\$
3. $\bigg( 1+ \dfrac{1}{2} \bigg) - \bigg( \dfrac{1}{51} + \dfrac{1}{52} \bigg) \\$
4. $1 - \bigg( \dfrac{1}{51} + \dfrac{1}{52} \bigg)$