This neat solution came from Marcos and the result was also proved by Yatir Halevi:
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By the binomial expansion:
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<img src="gif01.gif" width="177" height="44" alt="" /> 




 
<br /><br />This can me proved by induction on m but I won't clutter this with unnecessary proofs.
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Putting in x= -1  we have
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<img src="gif02.gif" width="155" height="44" alt="" /> 




 
<br /><br /> Dividing through by 



<em>m!</em> 



 
gives us the required result:
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<img src="gif03.gif" width="125" height="47" alt="" />