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ln(n^3)/n^3+1

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  • Sum of series:
  • e^-sqrt(n)/sqrt(n) e^-sqrt(n)/sqrt(n)
  • (2^n+3^n)/n^6 (2^n+3^n)/n^6
  • ln(n^3)/n^3+1 ln(n^3)/n^3+1
  • (1+n)/(2+n) (1+n)/(2+n)

  • Identical expressions

  • ln(n^ three)/n^ three + one
  • ln(n cubed ) divide by n cubed plus 1
  • ln(n to the power of three) divide by n to the power of three plus one
  • ln(n3)/n3+1
  • lnn3/n3+1
  • ln(n³)/n³+1
  • ln(n to the power of 3)/n to the power of 3+1
  • lnn^3/n^3+1
  • ln(n^3) divide by n^3+1

  • Similar expressions

  • ln(n^3)/n^3-1
Sum of series/ ln(n^3)/n^3+1

Sum of series ln(n^3)/n^3+1


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The solution

You have entered [src] 
  oo               
____               
\   `              
 \    /   / 3\    \
  \   |log\n /    |
   )  |------- + 1|
  /   |    3      |
 /    \   n       /
/___,              
n = 1
$$\sum_{n=1}^{\infty} \left(1 + \frac{\log{\left(n^{3} \right)}}{n^{3}}\right)$$ 
Sum(log(n^3)/n^3 + 1, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$1 + \frac{\log{\left(n^{3} \right)}}{n^{3}}$$
It is a series of species
$$a_{n} \left(c x - x_{0}\right)^{d n}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}$$
In this case
$$a_{n} = 1 + \frac{\log{\left(n^{3} \right)}}{n^{3}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\left|{1 + \frac{\log{\left(n^{3} \right)}}{n^{3}}}\right|}{1 + \frac{\log{\left(\left(n + 1\right)^{3} \right)}}{\left(n + 1\right)^{3}}}\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
Numerical answer
The series diverges
The graph
Sum of series ln(n^3)/n^3+1

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