1/4+1/28+1/70+…1/89698=?
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1/4+1/28+1/70+…1/89698=?
1/4+1/28+1/70+…1/89698=?
1/4+1/28+1/70+…1/89698=?
1/4+1/28+1/70+…1/89698
=1/3×(1-1/4+1/4-1/7+1/7-1/10+...+1/298-1/301)
=1/3×(1-1/301)
=100/301
1/4=(1-1/4)×1/3
1/28=(1/4-1/7)×1/3
1/70=(1/7-1/10)×1/3
……
1/89698=(1/298-1/301)×1/3
得:1/4+1/28+1/70+…1/89698
=(1-1/4)×1/3+(1/4-1/7)×1/3+(1/7-1/10)×1/3+……+(...
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1/4=(1-1/4)×1/3
1/28=(1/4-1/7)×1/3
1/70=(1/7-1/10)×1/3
……
1/89698=(1/298-1/301)×1/3
得:1/4+1/28+1/70+…1/89698
=(1-1/4)×1/3+(1/4-1/7)×1/3+(1/7-1/10)×1/3+……+(1/298-1/301)×1/3
=(1-1/4+1/4-1/7+1/7-1/10+……+1/298-1/301)×1/3
=(1-1/301)×1/3……裂项抵消
=300/301×1/3
=100/301
(望采纳,谢谢)
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1/4 看成(1-1/4)÷3
1/28看成(1/4-1/7) ÷3
1/70看成(1/7-1/10)÷3
。。。。。。。。
1/89698看成 (1/298-1/301)÷3
(1-1/4)÷3 +(1/4-1/7) ÷3+(1/7-1/10)÷3。。。。。。。。+(1/298-1/301)÷3
=[(1-1/4) +(1/4-1/7) +(1...
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1/4 看成(1-1/4)÷3
1/28看成(1/4-1/7) ÷3
1/70看成(1/7-1/10)÷3
。。。。。。。。
1/89698看成 (1/298-1/301)÷3
(1-1/4)÷3 +(1/4-1/7) ÷3+(1/7-1/10)÷3。。。。。。。。+(1/298-1/301)÷3
=[(1-1/4) +(1/4-1/7) +(1/7-1/10)。。。。。。。。+(1/298-1/301)]÷3
=[1-1/301]÷3
=300/301÷3
=100/301
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1/n(n+3)=1/3[1/n-1/(n+3)]
1/4+1/28+1/70+…1/89698=1/1×4+1/4×7+1/7×10+1/10×13+....+1/298×301
=1/3(1-1/4)+1/3(1/4-1/7)+1/3(1/7-1/10)+1/3(1/10-1/13)+...+1/3(1/298-1/301)
=1/3(1-1/3+1/3-1/7+1/7-1/10+1/10-1/13+...+1/298-1/301)
=1/3(1-1/301)
=100/301