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  "body": "\n## Definition\n\nA [[real sequence|0CTV783HYT]] $(a_n)$ is divergent if it is not a [[convergent sequence|0AZ3R52593]].\nThus, for each real number $L$, the sequence $(a_n)$ does not converge to $L$.\n\n## Remarks\n\nThe sequence $a_n = (-1)^n$ is divergent, and it is bounded.\nThe sequence $a_n = n$ is divergent, and it [[tends to infinity|09AZCV6GMC]].\nSome texts say that a sequence that tends to $+\\infty$ diverges to $+\\infty$. It is still divergent in the sense of this definition.\n\n## Explanations\n\n### L1 human\n\nA divergent sequence has no limit.\nIts terms can grow without bound, as in $1, 2, 3, \\dots$, or they can jump between values, as in $1, -1, 1, -1, \\dots$.\n",
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