Hi, I can't figure out how to arrive at the correct answer. Please help.

In the sequence a sub 1 (first term), a sub 2 (second term), a sub 3 (third term)….., a sub 100 (100th term), the k th term is defined by a sub k = 1/k - 1/(k+1) for all integers k from 1 through 100. What is the sum of the 100 terms of this sequence?

The answer is 100/101

## 1 Explanation