if the formula represent probabilities, then the sum of all probabilities
must equal 1.
These are sums to infinity.
n=1, 2, 3....
the sum of these "probabilities" is
which is a geometric series, first term 2/3, common ratio 1/3, whose sum to infinity is
All probabilities sum to 1, hence the function g(n) is valid.
For (ii), use the hint
Hence, the sum is
As this is 1, this function is also valid.