The support of a continuous random variables is $\text{{$u;f_X(u)>0$}}$.
This clue has been provided: "A theorem states that the sequence $(E[X^n])_n$ for all natural $n$ completely characterises the distribution of random variables with bounded support; in other words two different distributions with bounded support differ in some of the moments.
Suppose $E[X^i]=\frac{1}{i+1}$ for all natural $i$. Find the distribution of $X$.
How on earth does one approach this problem? The clue has only confused me.
So far all I have ascertained is that the sequence in question is $$(E[X^n])_n=\frac{1}2,\frac{1}3,\frac{1}4...\frac{1}n$$ How do I approach this?