JEE Mains · Maths · STD 11 - 12. limits
The value of \(\operatorname{Lim}_{n \rightarrow \infty} \frac{1+2-3+4+5-6+\ldots+(3 n-2)+(3 n-1)-3 n}{\sqrt{2 n^4+4 n+3-} \sqrt{n^4+5 n+4}}\) is :
- A \(\frac{\sqrt{2}+1}{2}\)
- B \(3(\sqrt{2}+1)\)
- C \(\frac{3}{2}(\sqrt{2}+1)\)
- D \(\frac{3}{2 \sqrt{2}}\)
Answer & Solution
Correct Answer
(C) \(\frac{3}{2}(\sqrt{2}+1)\)
Step-by-step Solution
Detailed explanation
\(\operatorname{Lim}_{n \rightarrow \infty} \frac{0+3+6+9+\ldots . n \text { terms }}{\sqrt{2 n^4+4 n+3}-\sqrt{n^4+5 n+4}}\) \(\operatorname{Lim}_{n \rightarrow \infty} \frac{3 n(n-1)}{2\left(\sqrt{2 n^4+4 n+3}-\sqrt{n^4+5 n+4}\right)}\)…
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