Question

Show that there does not exist any number C such that the following function would be a probability mass function (p.m.f)
f(x)=C/x, for x=1,2,3,4,...
0 elsewhere...

Answer 1

did you try taking \(\sum_{n=1}^{\infty}\frac{C}{n}\)?

Answer 2

yes i did

Answer 3

which is the same as
\[C\sum_{n=1}^{\infty}\frac{1}{n}\]

Answer 4

series does not converge, so it cannot be 1

Answer 5

yw