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(6*n-7)/2^n

  • How to use it?

  • Sum of series:
  • x^n/n
  • 1/(4n^2-1) 1/(4n^2-1)
  • 3/n 3/n
  • log((n+2)/n)^((-1)^(n+1)) log((n+2)/n)^((-1)^(n+1))

  • Identical expressions

  • (six *n- seven)/ two ^n
  • (6 multiply by n minus 7) divide by 2 to the power of n
  • (six multiply by n minus seven) divide by two to the power of n
  • (6*n-7)/2n
  • 6*n-7/2n
  • (6n-7)/2^n
  • (6n-7)/2n
  • 6n-7/2n
  • 6n-7/2^n
  • (6*n-7) divide by 2^n

  • Similar expressions

  • (6*n+7)/2^n
Sum of series/ (6*n-7)/2^n

Sum of series (6*n-7)/2^n


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The solution

You have entered [src] 
  oo         
____         
\   `        
 \    6*n - 7
  \   -------
  /       n  
 /       2   
/___,        
n = 1
$$\sum_{n=1}^{\infty} \frac{6 n - 7}{2^{n}}$$ 
Sum((6*n - 7)/2^n, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{6 n - 7}{2^{n}}$$
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
$$a_{n} = 6 n - 7$$
and
$$x_{0} = -2$$
,
$$d = -1$$
,
$$c = 0$$
then
$$\frac{1}{R} = \tilde{\infty} \left(-2 + \lim_{n \to \infty} \left|{\frac{6 n - 7}{6 n - 1}}\right|\right)$$
Let's take the limit
we find
False

$$R = 0$$
The rate of convergence of the power series
The answer [src] 
5
$$5$$ 
5
Numerical answer [src] 
5.00000000000000000000000000000
5.00000000000000000000000000000
The graph
Sum of series (6*n-7)/2^n

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