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根式裂项
\(\frac{1}{\sqrt{n}+\sqrt{n+1}}=\sqrt{n+1}-\sqrt{n}\)
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分数裂项
\(\frac{1}{n(n+1)}=\frac{1}{n}-\frac{1}{n+1}\)
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倒数平方裂项
\(\frac{2n+1}{n^2(n+1)^2}=\frac{1}{n^2}-\frac{1}{(n+1)^2}\)
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平方裂项
\(2n-1=(n+1)^2-n^2\)
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立方裂项
\(3n^2+3n+1=(n+1)^3-n^3\)
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对数裂项
根式裂项
\(\frac{1}{\sqrt{n}+\sqrt{n+1}}=\sqrt{n+1}-\sqrt{n}\)
分数裂项
\(\frac{1}{n(n+1)}=\frac{1}{n}-\frac{1}{n+1}\)
倒数平方裂项
\(\frac{2n+1}{n^2(n+1)^2}=\frac{1}{n^2}-\frac{1}{(n+1)^2}\)
平方裂项
\(2n-1=(n+1)^2-n^2\)
立方裂项
\(3n^2+3n+1=(n+1)^3-n^3\)
对数裂项