Math miscellaneousHard

Question

Let L = 2C0 + C2 + ..... + . Cn (where Cr = nCr). If S = , then which of the following is/are incorrect ?

Options

A.S is prime
B.S is composite
C.S is even
D.S is odd

Solution

(1 + t)n = C0 + C1t + C2t2 + .... + Cntn
(1 + t)ndt = (C0 + C1t + C2t2 + ..... + Cntn)dt


Differentiating w.r.t. x
 
= 2C0x + C2x3 + .... + CnXn+1
Put x = 1
⇒  L =
⇒ S = = 1

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