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?

Solution

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