lean_workbook_plus_60317

The common approach is to use telescoping sums. Let's look at the general term: the $n$ th term is $\frac{1}{n(n+1)}$ . We know that for telescoping sums to help, we need to express the general terms as a difference, so the terms can cancel out. We know that $\frac{1}{n(n+1)} = \frac{A}{n} + \frac{B}{n+1}$ for some real $A$ and $B$ . Solving, we see that $A=1$ and $B=-1$ . Now we can use telescoping sums to find our answer. We have $1/1 - 1/2 + 1/2 - 1/3 + ... +1/49 - 1/50$ . We see a lot of terms canceling out, leaving us with $1 - \frac{1}{50} = \boxed{\frac{49}{50}}$ as our answer .