(11/1*3)+(11/3*5)+(11/5*7)+.+(11/1989*1991)11/n(n+2)=./代表除 *代表乘假分数请化成带分数,please!

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(11/1*3)+(11/3*5)+(11/5*7)+.+(11/1989*1991)11/n(n+2)=./代表除 *代表乘假分数请化成带分数,please!
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(11/1*3)+(11/3*5)+(11/5*7)+.+(11/1989*1991)11/n(n+2)=./代表除 *代表乘假分数请化成带分数,please!
(11/1*3)+(11/3*5)+(11/5*7)+.+(11/1989*1991)
11/n(n+2)=.
/代表除 *代表乘
假分数请化成带分数,please!

(11/1*3)+(11/3*5)+(11/5*7)+.+(11/1989*1991)11/n(n+2)=./代表除 *代表乘假分数请化成带分数,please!
(11/1*3)+(11/3*5)+(11/5*7)+.+(11/1989*1991)
=11*[(1/1*3)+(1/3*5)+(1/5*7)+.+(1/1989*1991)]
=11*[1/2*(1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+.+1/2*(1/1989-1/1991)]
=11/2*[(1-1/3)+(1/3-1/5)+(1/5-1/7)+.+(1/1989-1/1991)]
=11/2*[1-1/1991]
=11/2*1990/1991
=10945/1991