hi everyone, can anyone help me on what looks like a simple problem?

i dont need you guys to do the whole problem, only hint or tell me how to begin : )

im working with E(e^t*N) = (e^-lambda)*[(sum of n = 0:infinity)*((lambda*e^t)^n))/n!]

this is equal to exp(lambda(e^t - 1))

how do you equal this to exp(lambda(e^t - 1)) ? geometric progression?

i am trying geometric progression formula = a/1-r

but getting nowhere : (

thank you all. sorry i dont have word or latex atm so i couldnt type the whole formula in maths form