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40(3/(7^n))^n

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  • Sum of series:
  • 6/(7*n^1) 6/(7*n^1)
  • 40(3/(7^n))^n 40(3/(7^n))^n
  • 24000 24000
  • 2*pi*(44+n*0.079) 2*pi*(44+n*0.079)

  • Identical expressions

  • forty (three /(seven ^n))^n
  • 40(3 divide by (7 to the power of n)) to the power of n
  • forty (three divide by (seven to the power of n)) to the power of n
  • 40(3/(7n))n
  • 403/7nn
  • 403/7^n^n
  • 40(3 divide by (7^n))^n
Sum of series/ 40(3/(7^n))^n

Sum of series 40(3/(7^n))^n


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The solution

You have entered [src] 
  oo          
____          
\   `         
 \           n
  \      /3 \ 
   )  40*|--| 
  /      | n| 
 /       \7 / 
/___,         
n = 1
$$\sum_{n=1}^{\infty} 40 \left(\frac{3}{7^{n}}\right)^{n}$$ 
Sum(40*(3/7^n)^n, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$40 \left(\frac{3}{7^{n}}\right)^{n}$$
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
$$a_{n} = 40 \left(3 \cdot 7^{- n}\right)^{n}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\left(3 \cdot 7^{- n}\right)^{n} \left(3 \cdot 7^{- n - 1}\right)^{- n - 1}\right)$$
Let's take the limit
we find
False

False
The rate of convergence of the power series
The answer [src] 
  oo             
 ___             
 \  `            
  \             n
   )     /   -n\ 
  /   40*\3*7  / 
 /__,            
n = 1
$$\sum_{n=1}^{\infty} 40 \left(3 \cdot 7^{- n}\right)^{n}$$ 
Sum(40*(3*7^(-n))^n, (n, 1, oo))
Numerical answer [src] 
17.2928214323922573040899044683
17.2928214323922573040899044683
The graph
Sum of series 40(3/(7^n))^n

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