Mister Exam

Other calculators

(-1)^n*ln(n/(n+1))

  • How to use it?

  • Sum of series:
  • (n+1)^2/2^(n-1) (n+1)^2/2^(n-1)
  • (-1)^n/n (-1)^n/n
  • cos(i*n)/2^n cos(i*n)/2^n
  • sin1/n sin1/n

  • Identical expressions

  • (- one)^n*ln(n/(n+ one))
  • ( minus 1) to the power of n multiply by ln(n divide by (n plus 1))
  • ( minus one) to the power of n multiply by ln(n divide by (n plus one))
  • (-1)n*ln(n/(n+1))
  • -1n*lnn/n+1
  • (-1)^nln(n/(n+1))
  • (-1)nln(n/(n+1))
  • -1nlnn/n+1
  • -1^nlnn/n+1
  • (-1)^n*ln(n divide by (n+1))

  • Similar expressions

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

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


∑
=

The solution

You have entered [src] 
  oo                  
 ___                  
 \  `                 
  \       n    /  n  \
   )  (-1) *log|-----|
  /            \n + 1/
 /__,                 
n = 1
$$\sum_{n=1}^{\infty} \left(-1\right)^{n} \log{\left(\frac{n}{n + 1} \right)}$$ 
Sum((-1)^n*log(n/(n + 1)), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\left(-1\right)^{n} \log{\left(\frac{n}{n + 1} \right)}$$
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
$$a_{n} = \log{\left(\frac{n}{n + 1} \right)}$$
and
$$x_{0} = 1$$
,
$$d = 1$$
,
$$c = 0$$
then
$$R = \tilde{\infty} \left(1 + \lim_{n \to \infty}\left(\frac{\log{\left(\frac{n}{n + 1} \right)}}{\log{\left(\frac{n + 1}{n + 2} \right)}}\right)\right)$$
Let's take the limit
we find
False
The rate of convergence of the power series
The graph
Sum of series (-1)^n*ln(n/(n+1))

    Examples of finding the sum of a series

    © Mister Exam – Calculator