小学奥数裂项计算，高手请进！
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解
1/(3²-1)+1/(5²-1)+……+1/(13²-1)
=1/(3-1)(3+1)+1/(5-1)(5+1)+……+1/(13-1)(13+1)
=1/(2×4)+1/(4×6)+……+1/(12×14)
=1/2(1/2-1/4)+1/2(1/4-1/6)+……+1/2(1/12-1/14)
=1/2[1/2+(1/4-1/4)+……+(1/12-1/12)-1/14]
=1/2(1/2-1/14)
=1/2(6/14)
=3/14
1/(3²-1)+1/(5²-1)+……+1/(13²-1)
=1/(3-1)(3+1)+1/(5-1)(5+1)+……+1/(13-1)(13+1)
=1/(2×4)+1/(4×6)+……+1/(12×14)
=1/2(1/2-1/4)+1/2(1/4-1/6)+……+1/2(1/12-1/14)
=1/2[1/2+(1/4-1/4)+……+(1/12-1/12)-1/14]
=1/2(1/2-1/14)
=1/2(6/14)
=3/14
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