Senin, 25 Oktober 2010

Salah satu soal g jelas

Ket : 2 maksudnya kuadrat, bukan basis 2
 (1-1/22)(1-1/32)(1-1/42)...(1-1/20062) =
Lakukan faktorisasi jadi :
(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)...(1-1/2006)(1+1/2006) =
(1/2)(3/2)(2/3)(4/3)(3/4)...(2005/2006)(2007/2006) =
tinggal dicoret :
(1/2)(3/2)(2/3)(4/3)(3/4)...(2005/2006)(2007/2006) =
(1/2)(2007/2006) = 2007/4012
Jadi,
 (1-1/22)(1-1/32)(1-1/42)...(1-1/20062) =2007/4012

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