找规律题:(1/(1*3))+(1/(2*4))+(1/(3*5)+...+(1/(9*11))的计算过程

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找规律题:(1/(1*3))+(1/(2*4))+(1/(3*5)+...+(1/(9*11))的计算过程
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找规律题:(1/(1*3))+(1/(2*4))+(1/(3*5)+...+(1/(9*11))的计算过程
找规律题:(1/(1*3))+(1/(2*4))+(1/(3*5)+...+(1/(9*11))的计算过程

找规律题:(1/(1*3))+(1/(2*4))+(1/(3*5)+...+(1/(9*11))的计算过程
1/1*3+1/2*4+1/3*5+1/4*6+……+1/9*11
=(2/1*3+2/2*4+2/3*5+2/4*6+……+2/9*11)/2
=[(1-1/3)+(1/2-1/4)+(1/3-1/5)+(1/4-1/6)+……+(1/8-1/10)+(1/9-1/11)]/2
=(1+1/2-1/10-1/11)/2
=36/55

(1/(1*3))+(1/(2*4))+(1/(3*5)+...+(1/(9*11))=1/2*(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+1/5-1/7+1/6-1/8+1/7-1/9+1/8-1/10+1/9-1/11)=1/2*(1+1/2-1/10-1/11)=36/55
分解后消去部分项,化简后求解。