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.
Rate this question :






















Prove that the product of 2n consecutive negative integers is divisible by (2n)!
RD Sharma - MathematicsThere are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.[Hint: Required number = 210 – 1].
Mathematics - ExemplarIf n+1Cr+1 : nCr = 11 : 6 and nCr : n–1Cr–1 = 6 : 3, find n and r.
RS Aggarwal - MathematicsIf nCr–1 = 36, nCr = 84 and nCr+1 = 126, find r.
RS Aggarwal - MathematicsFill in the Blanks
If nPr = 840, nCr = 35, then r = ______.
Mathematics - ExemplarThe number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them is
Mathematics - ExemplarTotal number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
Mathematics - Exemplar