Limn -n2-12-n2-n2-22-n2-n2-32-n2-n terms-

The correct option is A π/4 Using definite integral as a limit of sum.Required limit =∫_0^1√(1 x^2)dx = π4 ...

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Standard Formulae - 1

limn →∞[√n2-1...

Question

$lim n \to \infty [\frac{\sqrt{n^{2} - 1^{2}}}{n^{2}} + \frac{\sqrt{n^{2} - 2^{2}}}{n^{2}} + \frac{\sqrt{n^{2} - 3^{2}}}{n^{2}} + \dots . n t e r m s] =$

\frac{π}{4}

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\frac{π}{2}

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\frac{π}{3}

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\frac{2 π}{4}

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{lim}_{n \to \infty} ⎡ ⎢ ⎢ ⎣ \frac{1}{n} + \frac{1}{\sqrt{n^{2} - 1^{2}}} + \frac{1}{\sqrt{n^{2} - 2^{2}}} + . . . . + \frac{1}{\sqrt{n^{2} - {(n - 1)}^{2}}} ⎤ ⎥ ⎥ ⎦

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