The 42 points $P_1, P_2, \ldots, P_{42}$ lie on a straight line in that order, such that the distance between $P_n$ and $P_{n+1}$ is $\frac{1}{n}$ for all $1 \leq n \leq 41$. What is the sum of the distances between every pair of these points? (Each pair of points is counted only once.)

Let's think step by step and output the final answer within \boxed{}.
user