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NDA2023MathematicsBinomial TheoremActual

Let (1+x)^n=1+T₁ x+T₂ x^2+T₃ x^3+ +T_n x^n What is 1-T₁+2 T₂-3 T₃+ +(-1)^n n T_n equal to?

Options

  1. A0
  2. B-2^ n -1
  3. Cn 2^ n -1
  4. D1

Correct answer

D. 1

Step-by-step solution

Putting, x=-1 in equation (i) in privious problem, we get aligned & n (1-1)^ n -1 = T ₁-2 ~T +3 ~T ₃-4 ~T ₄+ .(-1)^ n -1 ~T _ n & 1- T ₁+2 ~T ₂-3 ~T ₃+4 ~T ₄+ +(-1)^ n ~T _ n =0+1=1 aligned

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