Suppose the claim frequency [math]N[/math] has a probability function defined recursively by

[[math]] \operatorname{P}(N=k) = a \operatorname{P}(N=k-1) [[/math]]

where [math]a\gt0[/math] and [math]k \geq 1 [/math]. Which of the following expressions equals the expected value of [math]N[/math]?

1. [math]a/(1-a)[/math]
2. [math]a [/math]
3. [math]a/(1-a^2)[/math]
4. [math]a^2/(1-a^2) [/math]
5. [math]1-a [/math]