GATE Civil Engineering
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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. $1 - \bigg( \dfrac{1}{51} + \dfrac{1}{52} \bigg)$
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