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  "body": "\n## Definition\n\nLet $(a_n)$ be a [[real sequence|0CTV783HYT]].\nThe sequence tends to $+\\infty$ if, for each real number $M$, there is a natural number $N$ such that $a_n \u003e M$ for all $n \\ge N$.\nThen the notation is $a_n \\to +\\infty$ as $n \\to \\infty$, or $\\lim_{n \\to \\infty} a_n = +\\infty$.\nThe sequence tends to $-\\infty$ if $-a_n \\to +\\infty$.\n\n## Remarks\n\nThe sequences $n$, $n^2$ and $2^n$ tend to $+\\infty$.\nA sequence that tends to $+\\infty$ is not bounded above, so it is a [[divergent sequence|01HR2AH0BX]].\nThe converse fails. The sequence $0, 1, 0, 2, 0, 3, \\dots$ is not bounded above, but it does not tend to $+\\infty$.\n\n## Explanations\n\n### L1 human\n\nA sequence tends to infinity when its terms become larger than any number you name, and stay larger.\nIt is not enough that the terms are sometimes large.\n",
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