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  • Sum of series:
  • sin(n*x)/n^3
  • ((8)(ln(x)))/(x^3)
  • 1/5 1/5
  • 1/nln(n)(ln(ln(n)))^p

  • Identical expressions

  • ((eight)(ln(x)))/(x^ three)
  • ((8)(ln(x))) divide by (x cubed )
  • ((eight)(ln(x))) divide by (x to the power of three)
  • ((8)(ln(x)))/(x3)
  • 8lnx/x3
  • ((8)(ln(x)))/(x³)
  • ((8)(ln(x)))/(x to the power of 3)
  • 8lnx/x^3
  • ((8)(ln(x))) divide by (x^3)
Sum of series/ ((8)(ln(x)))/(x^3)

Sum of series ((8)(ln(x)))/(x^3)


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The solution

You have entered [src] 
  oo          
____          
\   `         
 \    8*log(x)
  \   --------
  /       3   
 /       x    
/___,         
n = 1
∑n=1∞8log⁡(x)x3\sum_{n=1}^{\infty} \frac{8 \log{\left(x \right)}}{x^{3}} 
Sum((8*log(x))/x^3, (n, 1, oo))
The radius of convergence of the power series
Given number:
8log⁡(x)x3\frac{8 \log{\left(x \right)}}{x^{3}}
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=8log⁡(x)x3a_{n} = \frac{8 \log{\left(x \right)}}{x^{3}}
and
x0=0x_{0} = 0
,
d=0d = 0
,
c=1c = 1
then
1=lim⁡n→∞11 = \lim_{n \to \infty} 1
Let's take the limit
we find
True

False
The answer [src] 
oo*log(x)
---------
     3   
    x
∞log⁡(x)x3\frac{\infty \log{\left(x \right)}}{x^{3}} 
oo*log(x)/x^3

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