Binomial Therom

If C₀, C₁, C₂, ........., C_n are the binomial coefficients, then

2 C₁+ 2 ³ C ₃ + 2 ⁵C ₅ +............... equals

(a) 3 ⁿ + (-1) ⁿ2 (b)3ⁿ - (-1) ⁿ2
(c) 3 ⁿ +12 (d)3 ⁿ -12

1 Answers

(1+x)ⁿ = C₀+C₁x + C₂x²+....+ C_nxⁿ

puting x= 2

and again putting x= -2 and subtracting the two obtained equations we get

3ⁿ-(-1)ⁿ2= 2C₁ +2³C₃+...+2ⁿC_n

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