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3^(n-1)/7^n

  • How to use it?

  • Sum of series:
  • (2*n-1)/2^n (2*n-1)/2^n
  • 1/((2n-1)(2n+1)) 1/((2n-1)(2n+1))
  • sin(n*x)/n^3
  • 1/3 1/3

  • Identical expressions

  • three ^(n- one)/ seven ^n
  • 3 to the power of (n minus 1) divide by 7 to the power of n
  • three to the power of (n minus one) divide by seven to the power of n
  • 3(n-1)/7n
  • 3n-1/7n
  • 3^n-1/7^n
  • 3^(n-1) divide by 7^n

  • Similar expressions

  • 3^(n+1)/7^n
Sum of series/ 3^(n-1)/7^n

Sum of series 3^(n-1)/7^n


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The solution

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

False

$$R = 0$$
The rate of convergence of the power series
The answer [src] 
1/4
$$\frac{1}{4}$$ 
1/4
Numerical answer [src] 
0.250000000000000000000000000000
0.250000000000000000000000000000
The graph
Sum of series 3^(n-1)/7^n

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