1\n(n+3)+1\(n+3)(n+6)+1\(n+6)(n+9)=1\2 n+18 n为正整数,求n的值
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![1\n(n+3)+1\(n+3)(n+6)+1\(n+6)(n+9)=1\2 n+18 n为正整数,求n的值](/uploads/image/z/4511764-28-4.jpg?t=1%5Cn%28n%2B3%29%2B1%5C%28n%2B3%29%28n%2B6%29%2B1%5C%28n%2B6%29%28n%2B9%29%3D1%5C2+n%2B18+n%E4%B8%BA%E6%AD%A3%E6%95%B4%E6%95%B0%2C%E6%B1%82n%E7%9A%84%E5%80%BC)
1\n(n+3)+1\(n+3)(n+6)+1\(n+6)(n+9)=1\2 n+18 n为正整数,求n的值
1\n(n+3)+1\(n+3)(n+6)+1\(n+6)(n+9)=1\2 n+18 n为正整数,求n的值
1\n(n+3)+1\(n+3)(n+6)+1\(n+6)(n+9)=1\2 n+18 n为正整数,求n的值
裂项相消法
1/3【1/n-1/(n+3)+1/(n+3)-1/(n+6)+1/(n+6)-1/(n+9)】=1/(2n+18)
1/3{1/n-1/(n+9)}==1/(2n+18)
交叉相乘
6n+54=n^2+9n
(n-6)(n+9)=0
所以n=6或-9
祝学习进步