Sunday, 12 June 2016

combinatorics - Prove by induction that sumlimitsnk=mnchoosekkchoosem=nchoosem2nm.


Prove by induction that \displaystyle\sum\limits_{k=m}^{\ n}{n\choose k}{k\choose m}={n\choose m}2^{n-m}.




I can't figure out what is the base case. Could someone show the steps?

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