Prove that for all integer n3, P(n+1,3)−P(n,3)=3P(n,2).
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We shall prove by mathematical induction.
For
Thus it is true for
Assume it is true for Then
We shall show that it is true for
That is, P(k+2,3)-P(k+1,3)=3P(k+1,2)
For the RHS
Since LHS=RHS, then it is true for
Hence,