不得不赞的e的超强近似

张文泰 posted @ 2010年5月21日 03:13 in Art of Science , 3454 阅读

$e\approx \left( 1+9^{-4^{7\times 6}}\right)^{3^{2^{85}}}$

这个近似使用了1~9的所有数字，而且精度出乎意料的高，达到了小数点后18, 457, 734, 525, 360, 901, 453, 873, 570位！但是仔细观察发现，其实9^{-4^{7\times 6}}=3^{2^{85}}，而e的极限形式是$\lim_{n \to \infty} (1 +1/n)^n$，所以一切都可以解释了。

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2022年8月24日 19:33

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