The value of -1-na n - 1-n-x-a - x - -x dx

The correct option is D a2 1n ...

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Sum of n Terms

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Question

The value of $\int_{\frac{1}{n}}^{\frac{a n - 1}{n}} \frac{\sqrt{x}}{\sqrt{a - x} + \sqrt{x}} d x$

\frac{n}{2}

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\frac{1}{2 n} (n a + 2)

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\frac{n a - 3}{2 n}

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\frac{a}{2} - \frac{1}{n}

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\int_{1 / n}^{(a n - 1) / n} \frac{\sqrt{x}}{\sqrt{a - x} + \sqrt{x}} d x

1^{2} + 3^{2} + 5^{2} \dots + (2 n - 1)^{2} = \frac{n}{x} (2 n - 1) (2 n + 1)

n \in N

x

{lim}_{n \to \infty} (\frac{n}{(n + 1) \sqrt{2 n + 1}} + \frac{n}{(n + 2) \sqrt{2 (2 n + 2)}} + \frac{n}{(n + 3) \sqrt{3 (2 n + 3)}} . . . . . + \frac{1}{2 n \sqrt{3}})

lim x \to 0^{-} \frac{[x] + [x^{2}] + [x^{3}] + . . . . + [x^{2 n + 1}] + n + 1}{1 + [x^{2}] + | x | + 2 x}

\in

1 - 2 n + \frac{2 n (2 n - 1)}{2!} - \frac{2 n (2 n - 1) (2 n - 1)}{3!} + . . . + (- 1)^{n - 1} \frac{2 n (n - 1) . . . (n + 2)}{(n - 1)}

= (- 1)^{n + 1} \frac{(2 n)}{2 (n!)^{2}},

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