P(k)=a^k=2 3 4 find value of a that makes this is a valid probability distribution

Sounds like you're asked to find such that



In other words, find that satisfies



We can factorize this as



In order that describes a probability distribution, require that for all , which means we can ignore the possibility of .

Let .




Multiply both sides by .



We want to find that removes the quartic and quadratic terms from the equation, i.e.



so the cubic above transforms to



Substitute and we get

Sorry i really need my points

Do you have answer choices?