Explanation of the natural constant E

Andrew Zhang
Nov 28, 2017

The natural constant e E comes from the bank's compound interest calculation.
Suppose the bank rules not to consider compound interest when the annual rate is 100%, that is, you have to deposit 100 pieces, a year later can get 200 dollars.
So when you think about compound interest, put in 100 bucks and how much money you can get in a year.
Can be a step by step solution, the first can be divided into an average of n time period, then a year after the money received should be
(1+100%n) n=100 (1+1n) n (1) (1+\frac{100\%}{n}) ^n=100 (1+\frac{1}{n}) ^n \tag{1}
Next, just ask for the limit.
Limn−>0100 (1+1n) n=100limn−>0 (1+1n) n=100e (2) \lim_{n->0}{} (1+\frac{1}{n}) ^n=100\lim_{n->0}{} (1+\ Frac{1}{n}) ^n=100e \tag{2}

E e also has many properties, such as the ex e^x Taylor expansion, the derivative or itself, e e in the complex character and so on