阅读以下材料:1/21/3=1/2-1/3;1/21/4=1/2(1/2-1/4);1/31/6=1&#

答案:2 悬赏:10 手机版

解决时间 2021-12-02 07:23

提问者网友：佞臣
2021-12-01 06:26

阅读以下材料:1/2*1/3=1/2-1/3;1/2*1/4=1/2*(1/2-1/4);1/3*1/6=1/3*(1/3-1/6) 更具以上规律，若有理数a、b

最佳答案

五星知识达人网友：老鼠爱大米
2021-12-01 07:08

a-1的绝对值+ b-3的绝对值=o
∴a=1 b=3
∴1/ab+1/(a+4)*1/(b+4)+1/(a+6)*1/(b+6)+......+1/(a+100)*1/(b+100)
=1/(1×3)+1/(5×7)+1/(7×9)+1/(9×11)+……+1/(101×103)
=1/2(1-1/3)+1/2(1/5-1/7)+(1/7-1/9)+(1/9-1/11)+……+1/2(1/101-1/103)
=1/2×[1-1/3+1/5-1/7+1/7-1/9+……+1/101-1/103]
=1/2×[1-1/3+1/5-1/103]
=1/2×(1-1/3)+1/2×(1/5-1/103)
=1/3+51/515
=668/1545

全部回答

1楼网友：迷人又混蛋
2021-12-01 08:14

∴a=1 b=3
∴1/ab+1/(a+4)*1/(b+4)+1/(a+6)*1/(b+6)+......+1/(a+100)*1/(b+100)
=1/(1×3)+1/(5×7)+1/(7×9)+1/(9×11)+……+1/(101×103)
=1/2(1-1/3)+1/2(1/5-1/7)+(1/7-1/9)+(1/9-1/11)+……+1/2(1/101-1/103)
=1/2×[1-1/3+1/5-1/7+1/7-1/9+……+1/101-1/103]
=1/2×[1-1/3+1/5-1/103]
=1/2×(1-1/3)+1/2×(1/5-1/103)
=1/3+51/515
=668/1545

参考资料：2010zzqczb

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阅读以下材料:1/2*1/3=1/2-1/3;1/2*1/4=1/2*(1/2-1/4);1/3*1/6=1&#

阅读以下材料:1/21/3=1/2-1/3;1/21/4=1/2(1/2-1/4);1/31/6=1&#