Question of the Day #13

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.

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