GRE Question of the Day (June 28)

The sequence of numbers \({a_1}\), \({a_2}\), \({a_3}\), . . . , \({a_n}\), . . . is defined by \({a_n}\)\({= \frac{{1}}{{n}} - \frac{{1}}{{(n+2)}}}\) for each integer \({n ≥ 1}\). What is the sum of the first 20 terms of this sequence?

A. \({(1+\frac{{1}}{{2}}) - \frac{{1}}{{20}}}\)

B. \({(1+\frac{{1}}{{2}}) - (\frac{{1}}{{21}}+\frac{{1}}{{22}})}\)

C. \({1 - (\frac{{1}}{{20}}+\frac{{1}}{{22}})}\)

D. \({1 - \frac{{1}}{{22}}}\)

E. \({\frac{{1}}{{20}} - \frac{{1}}{{22}}}\)