inakihernandez wrote:
For every positive integer n, the nth term of sequence is given by an= 1/n - 1/(n+1). What is the sum of the first 100 terms?
(a) 1
(b) 0
(c) 25
(d) 99/100
(e) 100/101
The POE method (for non-genius like me):
a(n)= 1/n - 1/(n+1) => a(1)=1/2, a(2)=1/6, a(3)=1/12 ... a(100)=1/100*101
The largest is a(1) =1/2 and other terms become so small that they are not able to add together another 1/2 to overcome 1, but the sum is still +ve so crossout A,B,C.
Since we have to sum all this stuff and the last term a(100)=1/100*101 with prime number 101 in denominator, there is a huge chance that exactly 101 will stay in denominator. So the answer is (E).
p.s. This is not the best way to solve problems on GMAT, and you still have to learn the concept to be confident, but this is an example of how to make a smart guess and move on.