Apa itu bilangan e? | MemorisePi

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The limit definition: (1 + 1/n)ⁿ → e

Table showing (1+1/n)^n converging to e

n	(1 + 1/n)ⁿ	Abstdan zu e
1	2,000000	0,71828
10	2,593742	0,12454
100	2,704814	0,01347
1 000	2,716924	0,00136
1 000 000	2,718281	0,0000014
∞	2,71828…	0

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e^x: the only function that is its own derivative

At x=1, the height of the curve is e ≈ 2.718 and the slope of the tangent is also e. No other base b^x has this property.

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Compound interest converges to e as compounding increases

Starting with $1 at 100% annual interest: compounding monthly gives $2.613, daily $2.714, every second $2.718. The limit as n→∞ is exactly e.

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Generate the digits of Euler's Number e

e has no final digit

Euler's Number e is irrational. Its decimal expansion never ends and never repeats. Every digit shown below is computed from the taylor series.

e = 1 + 1/1! + 1/2! + 1/3! +...