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  • (-1)x(-2)x(-3)+(-2)x(-3)x(-4)+……+(-100)x(-101)x(-102)

    (-1)x(-2)x(-3)+(-2)x(-3)x(-4)+……+(-100)x(-101)x(-102)
    數(shù)學(xué)人氣:101 ℃時(shí)間:2020-04-25 19:28:23
    優(yōu)質(zhì)解答
    令Sn=1*2*3+2*3*4+.+n*(n+1)(n+2)
    =1/4[(1*2*3*4-0*1*2*3)+(2*3*4*5-1*2*3*4)+.+
    n(n+1)(n+2)(n+3)-(n-1)n(n+1)(n+2)]
    =1/4*n(n+1)(n+2)(n+3)
    (-1)x(-2)x(-3)+(-2)x(-3)x(-4)+……+(-100)x(-101)x(-102)
    =-S100
    =-1/4x100x101x102x103=-26527650
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