六年级奥数巧算题 1/(2*3*4)+1/(3*4*5)+1/(4*5*6)+.+1/(8*9*10)
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六年级奥数巧算题 1/(2*3*4)+1/(3*4*5)+1/(4*5*6)+.+1/(8*9*10)
![六年级奥数巧算题 1/(2*3*4)+1/(3*4*5)+1/(4*5*6)+.+1/(8*9*10)](/uploads/image/z/14321911-31-1.jpg?t=%E5%85%AD%E5%B9%B4%E7%BA%A7%E5%A5%A5%E6%95%B0%E5%B7%A7%E7%AE%97%E9%A2%98+1%2F%EF%BC%882%2A3%2A4%EF%BC%89%2B1%2F%EF%BC%883%2A4%2A5%EF%BC%89%2B1%2F%EF%BC%884%2A5%2A6%EF%BC%89%2B.%2B1%2F%EF%BC%888%2A9%2A10%EF%BC%89)
1/(2*3*4)+1/(3*4*5)+1/(4*5*6)+.+1/(8*9*10)
=1/2*[1/2-2/3+1/4+1/3-2/4+1/5+1/4-2/5+1/6...+1/8-2/9+1/10]
=1/2*[1/2-1/3-1/9+1/10]
=7/90
=1/2*[1/2-2/3+1/4+1/3-2/4+1/5+1/4-2/5+1/6...+1/8-2/9+1/10]
=1/2*[1/2-1/3-1/9+1/10]
=7/90
六年级奥数巧算题 1/(2*3*4)+1/(3*4*5)+1/(4*5*6)+.+1/(8*9*10)
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