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$$m^n=\sum_{i=0}^n(m-1)^i\binom{n}i$$

(a) I want to find a formula for the above and then prove it by induction. But there is two variable right those are $m$ and $n$. I know that this is true, however I have no idea how to get there. Any hints or ideas on how I should tackle this one?

all this means that

$$m^n=\sum_{i=0}^n(m-1)^i\binom{n}i=\sum_{j=0}^n\sum_{i=0}^n\left((m-2)^i\binom{n}i\right)^j\binom{n}j$$

3 Answers 3