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diverge




If a sequence doesn't converge it is said to diverge. This can be if it goes to infinity, or if it simply cycles between two or more values without ever staying on one of them. For example, the sequences: 1, 2, 4, 8, 16, 32, ... and 1, 0, 1, 0, 1, 0, ... are both divergent. Although not immediately obvious, the harmonic series, 1 + 1/2 + 1/3 + 1/4 + ... (see harmonic sequence) is also divergent.


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   • CALCULUS AND ANALYSIS
   • SERIES AND SEQUENCES