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(1+1/n)^n
Sum of series/ (1+1/n)^n

Sum of series (1+1/n)^n


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  oo          
____          
\   `         
 \           n
  \   /    1\ 
  /   |1 + -| 
 /    \    n/ 
/___,         
n = 1
$$\sum_{n=1}^{\infty} \left(1 + \frac{1}{n}\right)^{n}$$ 
Sum((1 + 1/n)^n, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\left(1 + \frac{1}{n}\right)^{n}$$
It is a series of species
$$a_{n} \left(c x - x_{0}\right)^{d n}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}$$
In this case
$$a_{n} = \left(1 + \frac{1}{n}\right)^{n}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\left(1 + \frac{1}{n}\right)^{n} \left(1 + \frac{1}{n + 1}\right)^{- n - 1}\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The graph
Sum of series (1+1/n)^n

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