Mister Exam

Other calculators

(n^2+5)/2^n

  • How to use it?

  • Sum of series:
  • 1/(n*(n+3)) 1/(n*(n+3))
  • (13^(2n-1))/((2^n)*(n-1)!) (13^(2n-1))/((2^n)*(n-1)!)
  • e^n/n^10 e^n/n^10
  • (n^2+5)/2^n (n^2+5)/2^n

  • Identical expressions

  • (n^ two + five)/ two ^n
  • (n squared plus 5) divide by 2 to the power of n
  • (n to the power of two plus five) divide by two to the power of n
  • (n2+5)/2n
  • n2+5/2n
  • (n²+5)/2^n
  • (n to the power of 2+5)/2 to the power of n
  • n^2+5/2^n
  • (n^2+5) divide by 2^n

  • Similar expressions

  • (n^2-5)/2^n
Sum of series/ (n^2+5)/2^n

Sum of series (n^2+5)/2^n


∑
=

The solution

You have entered [src] 
  oo        
____        
\   `       
 \     2    
  \   n  + 5
   )  ------
  /      n  
 /      2   
/___,       
n = 1
∑n=1∞n2+52n\sum_{n=1}^{\infty} \frac{n^{2} + 5}{2^{n}} 
Sum((n^2 + 5)/2^n, (n, 1, oo))
The radius of convergence of the power series
Given number:
n2+52n\frac{n^{2} + 5}{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=n2+5a_{n} = n^{2} + 5
and
x0=−2x_{0} = -2
,
d=−1d = -1
,
c=0c = 0
then
1R=∞~(−2+lim⁡n→∞(n2+5(n+1)2+5))\frac{1}{R} = \tilde{\infty} \left(-2 + \lim_{n \to \infty}\left(\frac{n^{2} + 5}{\left(n + 1\right)^{2} + 5}\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 (n^2+5)/2^n

    Examples of finding the sum of a series

    © Mister Exam – Calculator