求解大神!数学啊!需要详细步骤谢谢!
4个回答
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原式
=(1-2+3-4+5-6+7-8+9)+(1/2 -5/6+1/12 -19/20 +1/30-41/42+1/56-71/72+1/90)
=4+(1/2-1+1/6+1/12-1+1/20+1/30-1+1/42+1/56-1+1/72+1/90)
=4-4+1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)+
1/(7×8)+1/(8×9)+1/(9×10)
=1 -1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1-1/10
=9/10
=(1-2+3-4+5-6+7-8+9)+(1/2 -5/6+1/12 -19/20 +1/30-41/42+1/56-71/72+1/90)
=4+(1/2-1+1/6+1/12-1+1/20+1/30-1+1/42+1/56-1+1/72+1/90)
=4-4+1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)+
1/(7×8)+1/(8×9)+1/(9×10)
=1 -1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1-1/10
=9/10
追问
善意的告诉你(1-2+3-4+5-6+7-8+9)=5 不是4所以你的答案比正确答案少1
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2015-08-15
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1+1/2-3+1/6+3+1/12-5+1/20+5+1/30-7+1/42+7+1/56-9+1/72+9+1/90
=1+1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1+(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)。。。+(1/9-1/10)
=2-1/10
=1.9
=1+1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1+(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)。。。+(1/9-1/10)
=2-1/10
=1.9
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虽然会,这也太麻烦了
追问
。。。
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