Most Important Selected Qs for JEE AdvancedMathematicsSequences and Series
For n 1 , Let G_n be the geometric mean of k 2 n : 1 k n then _ n G_n equals:
Options
- A_ x 0 1- x x
- B_ x 0 1- x x^2
- C2 ₀^ / 2 ^2 x d x
- D_ x 0⁻ [ e^x-1 x ] [Note: [k] denotes greatest integer function less than or equal to k .]
Correct answer
C. 2 ₀^ / 2 ^2 x d x
Step-by-step solution
aligned & G_n= ( _ k=1 ^n k 2 n )^ 1 / n & aligned (G_n ) & = _ n 1 n _ k=1 ^n ( k 2 n ) & = ₀^1 ( x 2 ) d x aligned aligned aligned & = 2 ₀^ / 2 ( ) d =- 2 _ n G_n & = 1 2 aligned