IIT JEE , AIEEE Forum - Mathematics , Algebra

neeraj_agarwal_1990

Question:

Let n be natural number and C₀ , C ₁, C₂ , ....., C_n be the binomial coefficients. Then (n + 2) C₀ 2 ^{n + 1} -(n + 1)C₁ 2 ⁿ + n . C₂ 2 ⁿ ^{- 1} +...... is equal to:

Options:

A.

4n

B.

4

C.

2n + 4

D.

4 + 4n

Answer

Answer:

C

Conjurer

Consider (x-1)^n+2 = Cox^n+2 - C1 x^n+1 ...

Differentiating we get

(n+2)(1)(x-1)^n+1 = (n+2)Cox^n+1 - (n+1)C1 x^n .....

Putting x = 2 , we get the desired result

=> n+2.

Why option C :( . Are you sure you have typed the power of 2 correctly, I think every power should be increased by 1 to get the required answer.Or simply by symmetry you can guess the answer.

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