Q. 20 D4.8( 5 Votes )

Let r and n

Answer :

Given that we need to prove nCr + 2nCr – 1 + nCr – 2 = n + 2Cr


Consider L.H.S,


We know that nCr + nCr + 1 = n + 1Cr + 1


nCr + 2nCr – 1 + nCr – 2 = (nCr + nCr – 1) + (nCr – 1 + nCr – 2)


nCr + 2nCr – 1 + nCr – 2 = n + 1Cr + n + 1Cr – 1


nCr + 2nCr – 1 + nCr – 2 = n + 2Cr


= R.H.S


L.H.S = R.H.S, thus proved.


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