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