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  "body": "\n## Statement\n\nLet $x$ be a real number with $x \\ge -1$, and let $n$ be a natural number.\nThen\n$$(1 + x)^n \\ge 1 + n x.$$\n\n## Remarks\n\nWhen $x \\neq 0$ and $n \\ge 2$, the inequality is strict.\nFor natural numbers $n$, the inequality also holds when $x \\ge -2$.\nA proof by [[induction|0ASJVEFA9J]] on $n$ multiplies $(1 + x)^n \\ge 1 + n x$ by $1 + x \\ge 0$ and uses $n x^2 \\ge 0$.\n\n## Explanations\n\n### L1 human\n\nA small growth rate $x$, applied $n$ times, gives at least $n$ times that growth.\nFor example, $1.1^{10}$ is at least $1 + 10 \\cdot 0.1 = 2$; its true value is about $2.59$.\nThe difference comes from the growth on the growth, which the right side ignores.\n",
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