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  • 1/ab+1/(a-1)(b-1)+1/(a-2)(b-2)+…+1/(a-2011)(b-2011)的值.(a=-2,b=-1)

    1/ab+1/(a-1)(b-1)+1/(a-2)(b-2)+…+1/(a-2011)(b-2011)的值.(a=-2,b=-1)
    數(shù)學人氣:785 ℃時間:2020-09-17 22:47:40
    優(yōu)質(zhì)解答
    當a=-2,b=-1時
    1/ab+1/(a-1)(b-1)+1/(a-2)(b-2)+……+1/(a-2011)(b-2011)
    =1/[-2×(-1)]+1/[-3×(-2)]+1/[-4×(-3)]+……+1/[-2013×(-2012)]
    =1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2012×2013)
    =1-1/2+1/2-1/3+1/3-1/4+……+1/2012-1/2013
    =1-1/2013
    =2012/2013
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