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(2)由前面得到a=2,b=1
所以,原式=1/(1×2)+1/(2×3)+……+1/(2016×2017)
=1-(1/2)+(1/2)-(1/3)+……+(1/2016)-(1/2017)
=1-(1/2017)
=2016/2017
(3)同上题,只不过每一项提出一个(1/4),得到原式
=(1/4)×[1/(1×2)+1/(2×3)+……+1/(1008×1009)]
=(1/4)×[1-(1/1009)]
=(1/4)×(1008/1009)
=252/1009
所以,原式=1/(1×2)+1/(2×3)+……+1/(2016×2017)
=1-(1/2)+(1/2)-(1/3)+……+(1/2016)-(1/2017)
=1-(1/2017)
=2016/2017
(3)同上题,只不过每一项提出一个(1/4),得到原式
=(1/4)×[1/(1×2)+1/(2×3)+……+1/(1008×1009)]
=(1/4)×[1-(1/1009)]
=(1/4)×(1008/1009)
=252/1009
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