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I'm having a bit of a problem with a probability question. The question is

Let X be a normal random variable with mean [itex]\mu[/itex] and variance [itex]\sigma^{2}[/itex]. Find E[(X -[itex]\mu[/itex])[itex]^{k}[/itex]] for all k = 1,2,...

I'm not really sure what to do and need some help to confirm how to approach the question. I've tried messing around with moment generating functions, using the binomial theorem to expand E[(X -[itex]\mu[/itex])[itex]^{k}[/itex]] and also have tried computing the expectation directly. Are any of these methods the correct way to progress?

Any help is much appreciated, thanks!