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(9*n-7)/2^n

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  • Sum of series:
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  • (1-x^4)^n/(n+2)
  • factorial(n)/(n^2+1) factorial(n)/(n^2+1)
  • 56724.3*10^-1 56724.3*10^-1

  • Identical expressions

  • (nine *n- seven)/ two ^n
  • (9 multiply by n minus 7) divide by 2 to the power of n
  • (nine multiply by n minus seven) divide by two to the power of n
  • (9*n-7)/2n
  • 9*n-7/2n
  • (9n-7)/2^n
  • (9n-7)/2n
  • 9n-7/2n
  • 9n-7/2^n
  • (9*n-7) divide by 2^n

  • Similar expressions

  • (9*n+7)/2^n
Sum of series/ (9*n-7)/2^n

Sum of series (9*n-7)/2^n


∑
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The solution

You have entered [src] 
  oo         
____         
\   `        
 \    9*n - 7
  \   -------
  /       n  
 /       2   
/___,        
n = 1
∑n=1∞9n−72n\sum_{n=1}^{\infty} \frac{9 n - 7}{2^{n}} 
Sum((9*n - 7)/2^n, (n, 1, oo))
The radius of convergence of the power series
Given number:
9n−72n\frac{9 n - 7}{2^{n}}
It is a series of species
an(cx−x0)dna_{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:
Rd=x0+lim⁡n→∞∣anan+1∣cR^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}
In this case
an=9n−7a_{n} = 9 n - 7
and
x0=−2x_{0} = -2
,
d=−1d = -1
,
c=0c = 0
then
1R=∞~(−2+lim⁡n→∞(∣9n−7∣9n+2))\frac{1}{R} = \tilde{\infty} \left(-2 + \lim_{n \to \infty}\left(\frac{\left|{9 n - 7}\right|}{9 n + 2}\right)\right)
Let's take the limit
we find
False

R=0R = 0
The rate of convergence of the power series
1.07.01.52.02.53.03.54.04.55.05.56.06.5020
The answer [src] 
11
1111 
11
Numerical answer [src] 
11.0000000000000000000000000000
11.0000000000000000000000000000
The graph
Sum of series (9*n-7)/2^n

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