Mister Exam

Other calculators

(1/n)^(n-3)
Sum of series/ (1/n)^(n-3)

Sum of series (1/n)^(n-3)


∑
=

The solution

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

False
The rate of convergence of the power series
The answer [src] 
  oo        
 ___        
 \  `       
  \    3 - n
  /   n     
 /__,       
n = 1
$$\sum_{n=1}^{\infty} n^{3 - n}$$ 
Sum(n^(3 - n), (n, 1, oo))
Numerical answer [src] 
4.29507862687843037097334808608
4.29507862687843037097334808608
The graph
Sum of series (1/n)^(n-3)

    Examples of finding the sum of a series

    © Mister Exam – Calculator