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Manipal MET2016MathematicsBinomial Theorem

If t_n= _ r=0 ^n 1 ( ^n C_r )^k and S_n= _ r=0 ^n r ( ^n C_r )^k , where k Z⁺ , then ⁻¹ ( S_n n t_n ) is

Options

  1. A6
  2. B3
  3. C4
  4. D2

Correct answer

B. 3

Step-by-step solution

S_n= 0 ( ^n C₀ )^k + 1 ( ^n C₁ )^k + 2 ( ^n C₂ )^k + + n ( ^n C_n )^k S_n= n ( ^n C₀ )^k + n-1 ( ^n C₁ )^k + n-2 ( ^n C₂ )^k + + 0 ( ^n C₀ )^k array ll & 2 S_n=n t_n & S_n n t_n = 1 2 array Now, ⁻¹ ( S_n n t_n )= ⁻¹ ( 1 2 )= 3

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