WBJEE · Maths · Limits
The value of
\(\lim _{n \rightarrow \infty} \sum_{r=1}^n \frac{r^3}{r^4+n^4} \text { is }\)
- A \(\frac{1}{2} \log _{\mathrm{e}}(1 / 2)\)
- B \(\frac{1}{4} \log _e(1 / 2)\)
- C \(\frac{1}{4} \log _{\mathrm{e}} 2\)
- D \(\frac{1}{2} \log _{\mathrm{e}} 2\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{4} \log _{\mathrm{e}} 2\)
Step-by-step Solution
Detailed explanation
Hints: \(\operatorname{Lt}_{n \rightarrow \infty} \cdot \sum \frac{n^3\left(\frac{r}{n}\right)^3}{n^4\left[\left(\frac{r}{n}\right)^4+1\right]}\)…
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