Let S n - 1 2n - 1 - 4 n 2 -1 - 1 - 4 n 2 -4 - 1 - 3 n 2 -2n-1 -n- N- if lim n- S n - then which of the following is defined

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Conditional Identities

Let S n = 1...

Question

Let $S_{n} = \frac{1}{2 n} + \frac{1}{\sqrt{4 n^{2} - 1}} + \frac{1}{\sqrt{4 n^{2} - 4}} + . . . . . . . . + \frac{1}{\sqrt{3 n^{2} + 2 n - 1}}, n \in N$ , if ${lim}_{n \to \infty} S_{n} = α$ then which of the following is defined

{sin}^{- 1} α

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{cos}^{- 1} α

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{sec}^{- 1} α

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c o s e c^{- 1} α

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Solution

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Similar questions

lim n \to \infty [\frac{1}{2 n} + \frac{1}{\sqrt{4 n^{2} - 1}} + \frac{1}{\sqrt{4 n^{2} - 4}} + . . . . + \frac{1}{\sqrt{3 n^{2} + 2 n - 1}}]

lim n \to \infty (\frac{1}{\sqrt{4 n^{2} - 1}} + \frac{1}{\sqrt{4 n^{2} - 4}} + . . . . + \frac{1}{\sqrt{4 n^{2} - 2 n}})

$I f \frac{2 s i n α}{1 + c o s α + s i n α} = y, t h e n \frac{1 - c o s α + s i n α}{1 + s i n α} i s e q u a l t o$

α

x^{4} = 1

△ (α) =

∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 α^{n} & α^{n + 1} & α^{n + 3} \frac{1}{α^{n + 1}} & \frac{1}{α^{n}} & 0 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣

S_{n} = [\frac{1}{1 + \sqrt{n}} + \frac{1}{2 + \sqrt{2 n}} + \dots + \frac{1}{n + \sqrt{n^{2}}}]

lim n \to \infty S_{n} =

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