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AP EAMCET201923 Apr 2019Morning ShiftMathematicsLimitsActual

( _ n 1 n [(n+1)(n+2) ) ((2 n)]^ 1 n = )

Options

  1. A1
  2. B0
  3. C( 2 e )
  4. D( 4 e )

Correct answer

D. ( 4 e )

Step-by-step solution

Let (P= _ n 1 n [(n+1)(n+2) (2 n)]^ 1 / n ) On applying ' ( ^ ) both sides, we get ( P= _ n 1 n [ ( n+1 n ) ( n+2 n ) ( n+n n ) ] ) ( aligned & = _ n 1 n _ r=1 ^n (1+ r n )= ₀^1 (1+x) d x & =[x (1+x)]₀^1- ₀^1 x 1+x d x & = 2-(x- (1+x))₀^1 & = 2-1+ 2 & = 4-1= ( 4 e ) P= 4 e aligned ) Hence, option (d) is correct.

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