What is the product 1-1-2 1-1-3 1-1-4 - 1-1-n equal to when simplified-

The correct option is A 1/n ( 1 1/2 ) ( 1 1/3 ) ( 1 1/4 )...... ( 1 1/n )=1/2×2/3×3/4× ......×n 2/n 1×n 1/n=1/n ...

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What is the p...

Question

What is the product $(1 - \frac{1}{2}) (1 - \frac{1}{3}) (1 - \frac{1}{4}) . . . . . . (1 - \frac{1}{n})$ equal to when simplified?

\frac{1}{n}

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1 + 2 (1 - 1 / n) + 3 {(1 - 1 / n)}^{2} + . . . . . . . . . \infty

(n > 0)

(1 + \frac{1}{2}) (1 + \frac{1}{3}) (1 + \frac{1}{4}) . . . . . . . . . . . . . . (1 + \frac{1}{n}) =

\frac{{2.3}^{n + 1} + {7.3}^{n - 1}}{3^{n + 2} - 2 {(\frac{1}{3})}^{1 - n}}

(1 - \frac{1}{3}) (1 - \frac{1}{4}) (1 - \frac{1}{5}) . . . (1 - \frac{1}{n})

lim n \to \infty \frac{(1 - \frac{1}{2^{2}}) (1 - \frac{1}{3^{2}}) (1 - \frac{1}{4^{2}}) \cdot \cdot \cdot (1 - \frac{1}{n^{2}})}{(1 - \frac{1}{2}) (1 - \frac{1}{3}) (1 - \frac{1}{4}) . (1 - \frac{1}{n})}

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