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-(16/2^n)*n

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  • Sum of series:
  • 2(1/(n^2+5n+6)) 2(1/(n^2+5n+6))
  • 1/(1+n^2) 1/(1+n^2)
  • (n^3+n+5)/(n+6) (n^3+n+5)/(n+6)
  • (0.15/0.05)^1.3 (0.15/0.05)^1.3

  • Identical expressions

  • -(sixteen / two ^n)*n
  • minus (16 divide by 2 to the power of n) multiply by n
  • minus (sixteen divide by two to the power of n) multiply by n
  • -(16/2n)*n
  • -16/2n*n
  • -(16/2^n)n
  • -(16/2n)n
  • -16/2nn
  • -16/2^nn
  • -(16 divide by 2^n)*n

  • Similar expressions

  • (16/2^n)*n
Sum of series/ -(16/2^n)*n

Sum of series -(16/2^n)*n


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The solution

You have entered [src] 
  oo       
 ___       
 \  `      
  \     n  
  /   -8 *n
 /__,      
n = 1
∑n=1∞−8nn\sum_{n=1}^{\infty} - 8^{n} n 
Sum((-8^n)*n, (n, 1, oo))
The radius of convergence of the power series
Given number:
−8nn- 8^{n} 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=−na_{n} = - n
and
x0=−8x_{0} = -8
,
d=1d = 1
,
c=0c = 0
then
R=∞~(−8+lim⁡n→∞(nn+1))R = \tilde{\infty} \left(-8 + \lim_{n \to \infty}\left(\frac{n}{n + 1}\right)\right)
Let's take the limit
we find
False
The rate of convergence of the power series
1.07.01.52.02.53.03.54.04.55.05.56.06.5-2000000020000000
The answer [src] 
-oo
−∞-\infty 
-oo
Numerical answer
The series diverges
The graph
Sum of series -(16/2^n)*n

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