1/(1*3)+1/(3*5)+1/(5*7)+.1/(2013*2015)

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1/(1*3)+1/(3*5)+1/(5*7)+.1/(2013*2015)1/(1*3)+1/(3*5)+1/(5*7)+.1/(2013*2015)1/(1*3)+1/(3*5)+1/(5*7)+

1/(1*3)+1/(3*5)+1/(5*7)+.1/(2013*2015)
1/(1*3)+1/(3*5)+1/(5*7)+.1/(2013*2015)

1/(1*3)+1/(3*5)+1/(5*7)+.1/(2013*2015)
1/(1*3)+1/(3*5)+1/(5*7)+……+1/(2013*2015)
=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+……+1/2(1/2013-1/2015)
=1/2(1-1/3+1/3-1/5+1/5-1/7+……+1/2013-1/2015)
=1/2(1-1/2015)
=1/2×2014/2015
=1007/2015
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原式=1/2[(1-1/3)+(1/3-1/5)+.....+(1/2013-1/2015)]
=1/2(1-1/2015)
=1007/2015

1007/2015
把1/(1×3)分解为1/2×(1-1/3)即可,以此类推