The $n th$ term of a sequence $a_1, a_2, a_3, \ldots, a_n$ is given by $a_n = \dfrac1{n(n+2)}.$ What is the sum

The $n th$ term of a sequence $a_1, a_2, a_3, \ldots, a_n$ is given by $a_n = \dfrac1{n(n+2)}.$ What is the sum of the first $20$ terms of the sequence?

(A) $\dfrac{300}{440}$

(B) $\dfrac{325}{462}$

(C) $\dfrac{303}{462}$

(D) $\dfrac{375}{450}$

(E) $\dfrac{650}{462}$

Answer: B

Source: e-GMAT

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