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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 T₁+T₂+T₃+ +T_n equal to ?

Options

  1. A2^ n
  2. B2^ n -1
  3. C2^ n -1
  4. D2^ n +1

Correct answer

B. 2^ n -1

Step-by-step solution

Putting x =1 in given statement (1+1)^ n =1+ T ₁+ T ₂ aligned & + T ₃+ + T _ n & ~T ₁+ T ₂+ T ₃+ .+ T _ n =2^ n -1 aligned

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