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JEE Main2004MathematicsBinomial TheoremActual

If S_n= _ r=0 ^n 1 ^n C_r and t_n= _ r=0 ^n r ^n C_r , then t_n S_n is equal to

Options

  1. A1 2 n
  2. B1 2 n-1
  3. Cn-1
  4. D2 n-1 2

Correct answer

A. 1 2 n

Step-by-step solution

t= _ r=0 ^n r ^n C_r = _ r=0 ^n n-r ^n C_ n-r = _ r=0 ^n n-r ^n C_r ( ^n C_r= ^n C_ n-r )2 t_n= _ r=0 ^n r+n-r ^n C_r = _ r=0 ^n n ^n C_r t_n= n 2 _ r=0 ^n 1 ^n C_r = n 2 S_n t_n S_n = n 2

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