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Irrational number e |
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Consider the binominal expansion of (1 + )n where n is a positive interger.
When n tends to infinity, tend to zero. Also, n! = The coefficient of the general term(the (r+1)th term) is :
We take
When x = 1, we have
or where
Discovery of Natural Logarithms 自然對數的發現 Consider a function
If we change the base of the logarithm from a to e, we have = 1. The logarithm with base e is called Natural Logarithm. Therefore, when
Hence, + C or where C' is a constant
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