A student asked me this question recently. I think this is from AMC.

There are 42 points $P_1, P_2, P_3, \ldots , P_{42}$ placed on a straight line so that each distance from $P_i$ to $P_{i+1}$ is $\frac{1}{i}$ where $1 \le i \le 41$. What is the sum of the distances between every pair of these points?
Note: EVERY PAIR.