Question

nCr+ncr-1+nCr-2=n+2 C r

Answer 1

nCr + 2(nCr-1) + nCr-2 = (n+1)Cr

The coefficient of second term must be '2'.

Kindly refer attachment for proof.

 

Answer 2

ⁿCₓ  + 2 * ⁿCₓ₋₁  + ⁿCₓ₋₂  = ⁿ⁺²Cₓ

Step-by-step explanation:

Correct Question should be

nCr + 2(ncr-1) + nCr-2 = n+2 C r

replacing r with x

ⁿCₓ  + 2 * ⁿCₓ₋₁  + ⁿCₓ₋₂  = ⁿ⁺²Cₓ

LHS

= ⁿCₓ  + 2 * ⁿCₓ₋₁  + ⁿCₓ₋₂  

=  ⁿCₓ  + ⁿCₓ₋₁  + ⁿCₓ₋₁  + ⁿCₓ₋₂  

using ⁿCₓ + ⁿCₓ₋₁ = ⁿ⁺¹Cₓ

= ⁿ⁺¹Cₓ + ⁿ⁺¹Cₓ₋₁

= ⁿ⁺²Cₓ

= RHS

QED

Proved

Learn more:

Prove the relation rC(n r)=nC(n-1 r-1) - Brainly.in

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