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n^3/2^n

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  • Sum of series:
  • n^3/2^n n^3/2^n
  • nx^(n+1)
  • 21 21
  • pi^(2*n)/factorial(2*n) pi^(2*n)/factorial(2*n)

  • Identical expressions

  • n^ three / two ^n
  • n cubed divide by 2 to the power of n
  • n to the power of three divide by two to the power of n
  • n3/2n
  • n³/2^n
  • n to the power of 3/2 to the power of n
  • n^3 divide by 2^n
Sum of series/ n^3/2^n

Sum of series n^3/2^n


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The solution

You have entered [src] 
  oo    
____    
\   `   
 \     3
  \   n 
   )  --
  /    n
 /    2 
/___,   
n = 1
∑n=1∞n32n\sum_{n=1}^{\infty} \frac{n^{3}}{2^{n}} 
Sum(n^3/2^n, (n, 1, oo))
The radius of convergence of the power series
Given number:
n32n\frac{n^{3}}{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=n3a_{n} = n^{3}
and
x0=−2x_{0} = -2
,
d=−1d = -1
,
c=0c = 0
then
1R=∞~(−2+lim⁡n→∞(n3(n+1)3))\frac{1}{R} = \tilde{\infty} \left(-2 + \lim_{n \to \infty}\left(\frac{n^{3}}{\left(n + 1\right)^{3}}\right)\right)
Let's take the limit
we find
False

R=0R = 0
The rate of convergence of the power series
1.07.01.52.02.53.03.54.04.55.05.56.06.5040
The answer [src] 
26
2626 
26
Numerical answer [src] 
26.0000000000000000000000000000
26.0000000000000000000000000000
The graph
Sum of series n^3/2^n

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