MHT CET · Maths · Limits
\(\lim _{n \rightarrow \infty}\left[\frac{1}{1-\mathrm{n}^4}+\frac{8}{1-\mathrm{n}^4}+\ldots \ldots \ldots \ldots . .+\frac{\mathrm{n}^3}{1-\mathrm{n}^4}\right]=\)
- A \(\frac{1}{4}\)
- B \(\frac{1}{2}\)
- C \(-\frac{1}{2}\)
- D \(-\frac{1}{4}\)
Answer & Solution
Correct Answer
(D) \(-\frac{1}{4}\)
Step-by-step Solution
Detailed explanation
\( \lim _{n \rightarrow \infty}\left[\frac{1^3+2^3+\ldots+n^3}{1-n^4}\right] \) \( = \lim _{n \rightarrow \infty}\left[\frac{\left(\frac{n(n+1)}{2}\right)^2}{1-n^4}\right] \)
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