Y has gamma distribution with parameters α, λ > 0.

pdf is f(y)= {(λ^α)(y^(α-1))(e^(-λy))}/Γ(α)

If Y1, Y2, ..., Yn are independent random samples from such a gamma distribution, show that their sum also has a gamma distribution and give the parameters.

I can find E(ΣYi) and Var(ΣYi) and this leads me to believe the parameters of ΣYi are nα, λ, but I don't understand how to write down a more thorough arguement than just my first guesses.