AP EAMCET20227 Jul 2022Morning ShiftMathematicsLimitsActual
_ 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