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2020^(n+1)/(n!)
  • How to use it?

  • Sum of series:
  • (2*n-1)/2^n (2*n-1)/2^n
  • x^n/n^2
  • cos(1/n) cos(1/n)
  • ln(1+1/n) ln(1+1/n)
  • Identical expressions

  • two thousand and twenty ^(n+ one)/(n!)
  • 2020 to the power of (n plus 1) divide by (n!)
  • two thousand and twenty to the power of (n plus one) divide by (n!)
  • 2020(n+1)/(n!)
  • 2020n+1/n!
  • 2020^n+1/n!
  • 2020^(n+1) divide by (n!)
  • Similar expressions

  • 2020^(n-1)/(n!)

Sum of series 2020^(n+1)/(n!)



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The solution

You have entered [src]
  oo           
____           
\   `          
 \        n + 1
  \   2020     
  /   ---------
 /        n!   
/___,          
n = 1          
$$\sum_{n=1}^{\infty} \frac{2020^{n + 1}}{n!}$$
Sum(2020^(n + 1)/factorial(n), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{2020^{n + 1}}{n!}$$
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
$$a_{n} = \frac{2020^{n + 1}}{n!}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(2020^{- n - 2} \cdot 2020^{n + 1} \left|{\frac{\left(n + 1\right)!}{n!}}\right|\right)$$
Let's take the limit
we find
False

False
The rate of convergence of the power series
The answer [src]
              2020
-2020 + 2020*e    
$$-2020 + 2020 e^{2020}$$
-2020 + 2020*exp(2020)
Numerical answer [src]
0.e+880
0.e+880
The graph
Sum of series 2020^(n+1)/(n!)

    Examples of finding the sum of a series