Mister Exam

Other calculators

ln(n/10)/(exp(n/10)+1)

  • How to use it?

  • Sum of series:
  • (w+1)/w
  • (-1)^n/n^2 (-1)^n/n^2
  • 3^n/n! 3^n/n!
  • (3/7)^n (3/7)^n

  • Identical expressions

  • ln(n/ ten)/(exp(n/ ten)+ one)
  • ln(n divide by 10) divide by ( exponent of (n divide by 10) plus 1)
  • ln(n divide by ten) divide by ( exponent of (n divide by ten) plus one)
  • lnn/10/expn/10+1
  • ln(n divide by 10) divide by (exp(n divide by 10)+1)

  • Similar expressions

  • ln(n/10)/(exp(n/10)-1)
Sum of series/ ln(n/10)/(exp(n/10)+1)

Sum of series ln(n/10)/(exp(n/10)+1)


∑
=

The solution

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

False

False
The rate of convergence of the power series
Numerical answer [src] 
-1.37608262262025570369140735551
-1.37608262262025570369140735551
The graph
Sum of series ln(n/10)/(exp(n/10)+1)

    Examples of finding the sum of a series

    © Mister Exam – Calculator