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ISI2020-MMA: 9

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Define $\text{A}_{j} =\displaystyle{} \sum  ^{n}_{i=1} i^{j}, j = 0, 1, 2, 3.$ Then.

$$\lim_{n \rightarrow \infty } \frac{\text{A}_{1} \text{A}_{2} }{\text{A}_{0} \text{A}_{3}}$$

is,

  1. $0$

  2. $\frac{1}{2}$

  3. $\frac{2}{3}$

  4. $1$

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