Limit of a sum as n tends to infinity using the formulas for sum of k and k^3

This type of question, asked 2 times: 21 Apr 2025 S2, 20 Apr 2026 S2. All 2 questions below, oldest first.

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Question 1
21 Apr 2025 S2
135 $\lim_{n\rightarrow \infty} \left\lbrack \frac{1}{1 -n^{4}}+\frac{8}{1 -n^{4}}+ \ldots\ldots\ldots\ldots +\frac{n^{3}}{1 -n^{4}} \right\rbrack=$
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Question 2
20 Apr 2026 S2
59 $\lim_{n \to \infty}\left[\dfrac{1}{1 - n^2} + \dfrac{2}{1 - n^2} + \ldots + \dfrac{n}{1 - n^2}\right]^3$
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