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Limits Continuity and Differentiability question

2024 · 6 Apr · Shift 2 · Q34

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JEE Main
Mathematics
Limits Continuity and Differentiability
2024 · 6 Apr · Shift 2 · Q34

Limits Continuity and Differentiability question

2024 · 6 Apr · Shift 2 · Q34

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

\lim_{n \rightarrow \infty} \frac{\left(1^2-1\right)(n-1)+\left(2^2-2\right)(n-2)+\cdots+\left((n-1)^2-(n-1)\right) \cdot 1}{\left(1^3+2^3+\cdots \cdots+n^3\right)-\left(1^2+2^2+\cdots \cdots+n^2\right)}

is equal to :

A
$\frac{2}{3}$
B
$\frac{1}{2}$
C
$\frac{3}{4}$
D
$\frac{1}{3}$

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