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exp(-0.01*n)
Sum of series/ exp(-0.01*n)

Sum of series exp(-0.01*n)


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The solution

You have entered [src] 
  oo      
____      
\   `     
 \     -n 
  \    ---
  /    100
 /    e   
/___,     
n = 1
$$\sum_{n=1}^{\infty} e^{- \frac{n}{100}}$$ 
Sum(exp(-n/100), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$e^{- \frac{n}{100}}$$
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
$$a_{n} = 1$$
and
$$x_{0} = - e$$
,
$$d = - \frac{1}{100}$$
,
$$c = 0$$
then
$$\frac{1}{\sqrt[100]{R}} = \tilde{\infty} \left(- e + \lim_{n \to \infty} 1\right)$$
Let's take the limit
we find
False

$$R = 0$$
The rate of convergence of the power series
The answer [src] 
   -1/100  
  e        
-----------
     -1/100
1 - e
$$\frac{1}{\left(1 - e^{- \frac{1}{100}}\right) e^{\frac{1}{100}}}$$ 
exp(-1/100)/(1 - exp(-1/100))
Numerical answer [src] 
99.5008333319444477513144841479
99.5008333319444477513144841479
The graph
Sum of series exp(-0.01*n)

    Examples of finding the sum of a series

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