用简便方法计算，要过程
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=1/(1*3)+1/(3*5)+1/(5*7)+...+1/(11*13)
=0.5*(3-1)/(1*3)+0.5*(5-3)/(3*5)+...+0.5*(13-11)/(11*13)
=0.5*(1-1/3)+0.5*(1/3-1/5)+...+0.5*(1/11-1/13)
=0.5*(1-1/3+1/3-1/5+...+1/11-1/13)
=0.5*(1-1/13)
=6/13
=0.5*(3-1)/(1*3)+0.5*(5-3)/(3*5)+...+0.5*(13-11)/(11*13)
=0.5*(1-1/3)+0.5*(1/3-1/5)+...+0.5*(1/11-1/13)
=0.5*(1-1/3+1/3-1/5+...+1/11-1/13)
=0.5*(1-1/13)
=6/13
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展开全部
1/3+1/15+1/35+1/63+1/99+1/143=1/3+1/(3*5)+1/(5*7)+1/(7*9)+1/(9*11)+1/(11*13)
=1/3+(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13)/2
=1/3+(1/3-1/13)/2
=1/3+1/6-1/26
=1/2-1/26
=6/13
=1/3+(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13)/2
=1/3+(1/3-1/13)/2
=1/3+1/6-1/26
=1/2-1/26
=6/13
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