AP EAMCET · Maths · Definite Integration
\(\lim _{n \rightarrow \infty} n^4\left[\frac{1}{n^5}+\frac{1}{\left(n^2+1\right)^{\frac{5}{2}}}+\frac{1}{\left(n^2+4\right)^{\frac{5}{2}}}+\frac{1}{\left(n^2+9\right)^{\frac{5}{2}}}+\ldots+\right]=\)
- A \(\frac{3}{4 \sqrt{2}}\)
- B \(\frac{3 \sqrt{2}}{4}\)
- C \(\frac{5}{6 \sqrt{2}}\)
- D \(\frac{5 \sqrt{2}}{6}\)
Answer & Solution
Correct Answer
(C) \(\frac{5}{6 \sqrt{2}}\)
Step-by-step Solution
Detailed explanation
Since, \(\lim _{n \rightarrow \infty} n^4\left[\frac{1}{n^5}+\frac{1}{\left(n^2+1\right)^{\frac{5}{2}}}+\frac{1}{\left(n^2+4\right)^{\frac{5}{2}}}+\ldots .+\frac{1}{\left(n^2+n^2\right)^{\frac{5}{2}}}\right]\)…
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