Is there a discrete distribution with support 1 2 3 such tha

Is there a discrete distribution with support 1, 2, 3,…, such that the value of the PMF at n is proportional to 1/n?

Solution

There can be a finite discrete point distribution, but not an infinite one. The reason is that the sum of series (1/n) diverges, irrespective of what constant factor it is multiplied with. But this sum must not diverge, instead it should converge to a constant. This divergence violated important property of probability distribution that sum of all probabilities should be 1.