Highly selective Backlog Qs for JEE MainMathematicsLimits

_ n ( 1^2 n^3+1^3 + 2^2 n^3+2^3 + + 1 2 n )=

Options

A2
B2 2
C1 2 2
D[3] 2

Correct answer

D. [3] 2

Step-by-step solution

L= _ n [ 1^2 n^3+1^3 + 2^2 n^3+2^3 + + n^2 n^3+n^3 ]= _ n _ r=1 ^n r^2 n^3+r^3 = _ n _ r=1 ^n r^2 n^3 (1+ r^3 n^3 ) = _ n 1 n _ r=1 ^n ( r n )^2 1+ ( r n )^3 = ₀^1 x^2 d x 1+x^3 = 1 3 2= [3] 2

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