The product 1 -1-n 1-1-n-1 1-1-n-2 - 1-1-2n equals

The correct option is A n 12n nbsp;( 1 1 / n nbsp;) ( 1 1 / n+1 nbsp;) ( 1 1 / n+2 nbsp;) _____( 1 1 / 2n nbsp;) = n 1 / n × n ...

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Elimination Method of Finding Solution of a Pair of Linear Equations

The product ...

Question

The product $(1 - \frac{1}{n}) (1 - \frac{1}{n + 1}) (1 - \frac{1}{n + 2}) . . . (1 - \frac{1}{2 n})$ equals

\frac{n - 1}{2 n}

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\frac{1}{2 n}

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\frac{2 n}{n - 1}

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\frac{1}{n}

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Solution

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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}},

a = \infty \sum n = 1 \frac{2 n}{(2 n - 1)!}, b = \infty \sum n = 1 \frac{2 n}{(2 n + 1)!}

a b

a = \infty \sum n = 1 \frac{2 n}{(2 n - 1)!}, b = \infty \sum n = 1 \frac{2 n}{(2 n + 1)!}

a b

\frac{1}{x}

(1 + x)^{n} {(1 + \frac{1}{x})}^{n}

1 + \frac{2 n}{3} + \frac{2 n (2 n + 2)}{3.6} + \frac{2 n (2 n + 2) (2 n + 4)}{3.6.9} + . . . . .

= 2^{n} {1 + \frac{n}{3} + \frac{n (n + 1)}{3.6} + \frac{n (n + 1) (n + 2)}{3.6.9} + . . . .}

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