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I'm trying to prove pascal's rule by induction.Who could tell me how can I prove the following equation. i.e $$\dbinom{n}{k}=\dbinom{n-1}{k-1}+\dbinom{n-1}{k}$$

Many Thanks!!!

JMP
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Yi Wang
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    See http://math.stackexchange.com/questions/20475/proving-pascals-rule-n-choose-r-n-1-choose-r-1n-1-choose and https://proofwiki.org/wiki/Pascal's_Rule – lab bhattacharjee May 29 '16 at 09:05
  • unfortunately,all the answers mentioned above are algebraic or combinatial proof ..I do need a proof by Induction..:-) – Yi Wang May 29 '16 at 09:28
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    @HenningMakholm et al The OP specifically asked for an induction proof. None of the answers to the question you quote as a duplicate give an induction proof, so why did you close? Given that this is a fundamental result, which can be proved by induction, I do not see that the question is unreasonable. – almagest May 29 '16 at 09:56

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