How to find the value of a variable in a probability distribution function? I encountered a mathematics problem that I don't know how to solve.
$P(X=x) = a(\frac{5}{6})^x$ is a probability distribution function for the probability distribution of the discrete random variable $X$ for $x = 0,1,2,3\dots$
I know that the summation of all probabilities will add up to one, but whenever I set up the summation notation, moving the a to the other side creating the fraction $\frac{1}{a}$, I end up with the summation being equal to $0$. I tried to calculate the summation using the geometric series sum formula, but using a first term of $0$ makes this equal to zero.
The answer given by the textbook is $\frac{1}{6}$, but I have no idea how to get there.

As you said in your question, we must have
$$ 1=\sum_{x=0}^{\infty}\mathbb{P}(X=x)=a\sum_{x=0}^{\infty}\Big(\frac{5}{6}\Big)^x$$
Using the formula for the sum of a geometric series, we obtain
$$ 1=\frac{a}{1-\frac{5}{6}}=\frac{a}{\frac{1}{6}}$$
so $a=\frac{1}{6}$.
