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# The product (1 - {1/2}^2)(1 - {1/3}^2)...(1 - {1/9}^2)(1 - {

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The product (1 - {1/2}^2)(1 - {1/3}^2)...(1 - {1/9}^2)(1 - { [#permalink]
My way was the long way, but the numerators can all be written as 1 less than the denominator, and the denominator is square of every number from 2 till 10:

3/4 * 8/9 * 15/16 * 24/25 * 35/36* 48/49 * 63/64* 80/81 *99/100

Cancelling out everything leaves 11/20. Took me around 2 mins though.
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Re: The product (1 - {1/2}^2)(1 - {1/3}^2)...(1 - {1/9}^2)(1 - { [#permalink]
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Re: The product (1 - {1/2}^2)(1 - {1/3}^2)...(1 - {1/9}^2)(1 - { [#permalink]
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