The same question was asked yesterday. Here's the link to the question. Look at the hint and try to solve.
Poisson distribution - help with question!
Let the random variable X have a Poisson distribution with parameter λ. Show that for every n greater than or equal to 1 one has E(X^n) = λ E((X +1)^(n-1)): Note that, using this formula, we can find E(X);E(X^2);....recursively.