Q. 20 D4.8( 5 Votes )
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
nCr + 2nCr – 1 + nCr – 2 = n + 2Cr
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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