Manipal MET2016MathematicsLimits

The value of _ n [ [3] n^2-n^3 +n ] is

Options

A1 3
B- 1 3
C2 3
D- 2 3

Correct answer

A. 1 3

Step-by-step solution

_ n [ [3] n^2-n^3 +n ]= _ n n [ (-1+ 1 n )^ 1 / 3 +1^ 1 / 3 ]= _ n n ( 1 n -1 )+1 ( 1 n -1 )^ 2 / 3 +1- ( 1 n -1 )^ 1 / 3 [ a+b= a^3+b^3 a^2-a b+b^2 ]= _ n 1 ( 1 n -1 )^ 2 / 3 +1- ( 1 n -1 )^ 1 / 3 = 1 1+1+1 = 1 3

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