3²+1/3²-1+5²+1/5²-1+7²+1/7²-1+…+2013²+1/2013²-1
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1/(3²-1)+1/(5²-1)+1/(7²-1)+……+1/(13²-1)
= 1/(3-1)(3+1) + 1/(5-1)(5+1)+....+1/(13-1)(13+1)
= 1/(2x4) + 1/(4x6) + .... + 1/(12x14)
= [1/2-1/4 + 1/4-1/6 + ... + 1/12-1/14]/2
=[1/2 - 1/14]/2
= 3/14
= 1/(3-1)(3+1) + 1/(5-1)(5+1)+....+1/(13-1)(13+1)
= 1/(2x4) + 1/(4x6) + .... + 1/(12x14)
= [1/2-1/4 + 1/4-1/6 + ... + 1/12-1/14]/2
=[1/2 - 1/14]/2
= 3/14
追问
题目不对哦
追答
(3²+1)/(3²-1)+(5²+1)/(5²-1)+(7²+1)/(7²-1)+…+(2013²+1)/(2013²-1)
=1+2/(3²-1)+1+2/(5²-1)+1+2/(7²-1)+……+1+2/(2013²-1)
=1006+2/(3-1)(3+1) + 2/(5-1)(5+1)+2/(7-1)(7+1)....+2/(2013-1)(2013+1)
=1006+ 2/(2x4) + 2/(4x6)+2/(6x8) + .... + 2/(2012x2014)
=1006+(1/2-1/4 + 1/4-1/6 + ... + 1/2012-1/2014)
=1006+(1/2-1/2014)
=1006又503/1007
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