For every positive integer n, the nth term of a sequence is given by a_{n} = \frac{1}{n} - \frac{1}{n + 1}. what is the sum of the first 100 terms of this sequence?

The sum telescopes nicely:

2 over 5

step-by-step explanation:

the 2: 3 ratio is the length of the ac segment to the cb segment total length. this implies that the ratio between segment ac length and segment ab length is 2: 5. point c is 2/5 from a to b, so the required fraction is 2/5.