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 constante de euler

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constante de euler

 Jan 18, 2015

Best Answer 

 #1
avatar+23247 
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Euler's constant:

\gamma = \lim_{n \rightarrow \infty } \left( \sum_{k=1}^n \frac{1}{k} - \ln(n) \right)=\int_1^\infty\left({1\over\lfloor x\rfloor}-{1\over x}\right)\,dx.

=  0.57721566490...

 

Euler's number:

e = \displaystyle\sum\limits_{n = 0}^{ \infty} \dfrac{1}{n!} = 1 + \frac{1}{1} + \frac{1}{1\cdot 2} + \frac{1}{1\cdot 2\cdot 3} + \cdots

=  2.71828182846...

 Jan 18, 2015

1+0 Answers

 #1
avatar+23247 
+5
Best Answer

Euler's constant:

\gamma = \lim_{n \rightarrow \infty } \left( \sum_{k=1}^n \frac{1}{k} - \ln(n) \right)=\int_1^\infty\left({1\over\lfloor x\rfloor}-{1\over x}\right)\,dx.

=  0.57721566490...

 

Euler's number:

e = \displaystyle\sum\limits_{n = 0}^{ \infty} \dfrac{1}{n!} = 1 + \frac{1}{1} + \frac{1}{1\cdot 2} + \frac{1}{1\cdot 2\cdot 3} + \cdots

=  2.71828182846...

geno3141 Jan 18, 2015

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