裂项求和法1/3+1/15+1/35+1/63+1/99=?

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裂项求和法1/3+1/15+1/35+1/63+1/99=?
裂项求和法
1/3+1/15+1/35+1/63+1/99=?

裂项求和法1/3+1/15+1/35+1/63+1/99=?
1/3+1/15+1/35+1/63+1/99
=[(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)]÷(3-1)
=[1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11]÷2
=(1-1/11)÷2
=5/11
裂项分拆:
1/(a×b)=(1/a-1/b)÷(b-a)

=1/(1*3)+1/(3*5)+....1/(9*11)
=1/2*[1/1-1/3+1/3-1/5+....+1/9-1/11]
=1/2*(1-1/11)
=5/11