1/3+1/15+1/35+1/63+1/99 用裂项法.
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![1/3+1/15+1/35+1/63+1/99 用裂项法.](/uploads/image/z/303338-2-8.jpg?t=1%2F3%2B1%2F15%2B1%2F35%2B1%2F63%2B1%2F99+%E7%94%A8%E8%A3%82%E9%A1%B9%E6%B3%95.)
1/3+1/15+1/35+1/63+1/99 用裂项法.
1/3+1/15+1/35+1/63+1/99 用裂项法.
1/3+1/15+1/35+1/63+1/99 用裂项法.
1/3+1/15+1/35+1/63+1/99
=1/(1*3)+1/(3*5)+1/(5*7)+1/(7*9)+1/(9*11)
=1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11
=1-1/11
=10/11
1/3+1/15+1/35+1/63+1/99
=1/2*(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=1/2*(1-1/11)
=1/2*10/11
=5/11