Explanation

Remember, the key to most GRE sequence questions is discovering a pattern among the terms. So start off by finding the first few terms and looking for a pattern.

\(a1 = 1 -\frac{1}{1+1}= 1-\frac{1}{2}\).
\(a2 = \frac{1}{2} -\frac{1}{2+1}= \frac{1}{2} - \frac{1}{3}\).
\(a3 = \frac{1}{3} -\frac{1}{3+1}= \frac{1}{3} - \frac{1}{4}\).

Hence sum \(a1 + a2 + a3 ....... = 1-\frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} + ......\)

So alternate terms terms cancel out. So

\(a100 = \frac{1}{100} - \frac{1}{101}\)

So \(a1 + a2 + a3 ...... a100\)=\(1 - \frac{1}{101} = \frac{100}{101}\).


Hence option D is correct.
_________________

Sandy
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