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ln(n+2)/n/1/(3n+7)^1/2

  • How to use it?

  • Sum of series:
  • n^2/3^n n^2/3^n
  • n^3/2^n n^3/2^n
  • (3/4)^n (3/4)^n
  • 1/((2n-1)*(2n+1)) 1/((2n-1)*(2n+1))

  • Identical expressions

  • ln(n+ two)/n/ one /(3n+ seven)^ one / two
  • ln(n plus 2) divide by n divide by 1 divide by (3n plus 7) to the power of 1 divide by 2
  • ln(n plus two) divide by n divide by one divide by (3n plus seven) to the power of one divide by two
  • ln(n+2)/n/1/(3n+7)1/2
  • lnn+2/n/1/3n+71/2
  • lnn+2/n/1/3n+7^1/2
  • ln(n+2) divide by n divide by 1 divide by (3n+7)^1 divide by 2

  • Similar expressions

  • ln(n+2)/n/1/(3n-7)^1/2
  • ln(n-2)/n/1/(3n+7)^1/2
Sum of series/ ln(n+2)/n/1/(3n+7)^1/2

Sum of series ln(n+2)/n/1/(3n+7)^1/2


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The solution

You have entered [src] 
   oo                 
______                
\     `               
 \      //log(n + 2)\\
  \     ||----------||
   \    |\    n     /|
    \   |------------|
    /   \     1      /
   /    --------------
  /        _________  
 /       \/ 3*n + 7   
/_____,               
 n = 1
$$\sum_{n=1}^{\infty} \frac{1^{-1} \frac{\log{\left(n + 2 \right)}}{n}}{\sqrt{3 n + 7}}$$ 
Sum(((log(n + 2)/n)/1)/sqrt(3*n + 7), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{1^{-1} \frac{\log{\left(n + 2 \right)}}{n}}{\sqrt{3 n + 7}}$$
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
$$a_{n} = \frac{\log{\left(n + 2 \right)}}{n \sqrt{3 n + 7}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\left(n + 1\right) \sqrt{3 n + 10} \log{\left(n + 2 \right)}}{n \sqrt{3 n + 7} \log{\left(n + 3 \right)}}\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
  oo               
____               
\   `              
 \      log(2 + n) 
  \   -------------
  /       _________
 /    n*\/ 7 + 3*n 
/___,              
n = 1
$$\sum_{n=1}^{\infty} \frac{\log{\left(n + 2 \right)}}{n \sqrt{3 n + 7}}$$ 
Sum(log(2 + n)/(n*sqrt(7 + 3*n)), (n, 1, oo))
Numerical answer [src] 
2.66039456310106764014285696179
2.66039456310106764014285696179
The graph
Sum of series ln(n+2)/n/1/(3n+7)^1/2

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