Math miscellaneousHard
Question
Let L = 2C0 + 
C2 + ..... + 
. Cn (where Cr = nCr). If S = 
, then which of the following is/are incorrect ?
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
(1 + t)ndt = (C0 + C1t + C2t2 + ..... + Cntn)dtDifferentiating w.r.t. x
= 2C0x +
C2x3 + .... + CnXn+1Put x = 1
⇒ L =
⇒ S =
= 1Create a free account to view solution
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