Wednesday, September 30, 2009

Product of fractions

Simplify (3/4)*(8/9)*(15/16)*(24/25)*...*(9999/10000).
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  1. DavidOctober 1, 2009 at 8:20 AM

    The answer is 101/200

    (3/4)(8/9)(15/16)...(9999/10000)
    = (1-1/4)(1-1/9)(1-1/16)...(1-1/10000)
    = (1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/100)(1+1/100)
    = (1/2)(3/2)(2/3)(4/3)(3/4)...(100/99)(99/100)(101/100)
    = (1/2)(101/100)
    = 101/200

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