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1/(5*6*7)+1/(6*7*8)+1/(7*8*9)+1/(8*9*10)
题目详情
1/(5*6*7)+1/(6*7*8)+1/(7*8*9)+1/(8*9*10)
▼优质解答
答案和解析
前2个通分 + 后2个通分
= (1/5 +1/8)*1/(6*7) +(1/7+1/10)*1/（8*9）
=13/(40*6*7) +17/(70*8*9)
=13/(5*6*7*8) +17/(5*6*7*8*3)
=(13*3+17)/(5*6*7*8*3)
=(56)/(5*6*7*8*3)
=1/90
或者1/n(n+1)(n+2)
= 1/2 [2/n(n+1)(n+2) ]
= 1/2 [ 1/n(n+1) - 1/(n+1)(n+2) ]
= 1/2 [1/n - 1/(n+1) - 1/(n+1) +1/(n+2) ]
= (1/5 +1/8)*1/(6*7) +(1/7+1/10)*1/（8*9）
=13/(40*6*7) +17/(70*8*9)
=13/(5*6*7*8) +17/(5*6*7*8*3)
=(13*3+17)/(5*6*7*8*3)
=(56)/(5*6*7*8*3)
=1/90
或者1/n(n+1)(n+2)
= 1/2 [2/n(n+1)(n+2) ]
= 1/2 [ 1/n(n+1) - 1/(n+1)(n+2) ]
= 1/2 [1/n - 1/(n+1) - 1/(n+1) +1/(n+2) ]
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