## 42 Points

From the 2007 Australian Maths Competition:

There are 42 points $P_1, P_2, ..., P_{42}$ , placed in order on a straight line so that each distance from $P_i$ to $P_{i+1}$ is  $\dfrac{1}{i}$  for $1\leq i\leq 41$. What is the sum of the distances between every pair of these points?