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NDA2018MathematicsBinomial TheoremActual

What is C(n, r)+2 C(n, r-1)+C(n, r-2) equal to?

Options

  1. AC ( n +1, r )
  2. BC ( n -1, r +1)
  3. CC(n, r+1)
  4. DC ( n +2, r )

Correct answer

D. C ( n +2, r )

Step-by-step solution

aligned & C(n, r)+2 C(n, r-1)+C(n, r-2) & = ^ n C _ r +2 ( ^ n C _ r -1 )+ ^ n C _ r -2 & = ^ n C _ r + ^ n C _ r -1 + ^ n C _ r -1 + ^ n C _ r -2 & ( ^ n C_r+ ^n C_ r-1 = ^ n+1 C_r ) aligned aligned & = ^ n+1 C_r+ n+1 r-1 & = ^ n+2 C_r=C(n+2, r) aligned

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