Limn-n-1-n-n is equal to

The correct option is B #10; 1/e #10; lim_n→∞(ni)^^1/_n/n lim_n→∞^1/_n log(^r/_n)=e∫_0^1logx dx ∫_0^1logx dx=xlogx x∫_0^1 =(1 log( ...

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Logarithmic Differentiation

limn→∞n!1/n/n...

Question

$lim n \to \infty \frac{(n!)^{1 / n}}{n}$ is equal to

e

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\frac{1}{e}

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e - 1

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e - 5

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Solution

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lim n \to \infty \frac{e^{- n}}{(1 + \frac{1}{n})}

lim n \to \infty \frac{1}{n} [e^{1 / n} + e^{2 / n} + \dots . . + e] = ?

f (x) = \frac{1}{n} {[(n + 1) (n + 2) (n + 3) . . . (n + n)]}^{\frac{1}{n}}

{lim}_{n \to \infty} f (x)

\frac{4}{e}

lim n \to \infty \frac{1}{n} f (\frac{r}{n}) = \int_{0}^{1} f (x) d x

lim n \to \infty \frac{1}{n} ⎛ ⎜ ⎝ 1 + e^{1 / n} + e^{2 / n} + . . . + e^{\frac{n - 1}{n}} ⎞ ⎟ ⎠

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

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