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1/n^4

  • How to use it?

  • Sum of series:
  • 1/n^4 1/n^4
  • n n
  • (n-1)/factorial(n) (n-1)/factorial(n)
  • 36 36

  • Identical expressions

  • one /n^ four
  • 1 divide by n to the power of 4
  • one divide by n to the power of four
  • 1/n4
  • 1/n⁴
  • 1 divide by n^4
Sum of series/ 1/n^4

Sum of series 1/n^4


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The solution

You have entered [src] 
  oo    
____    
\   `   
 \    1 
  \   --
  /    4
 /    n 
/___,   
n = 1
$$\sum_{n=1}^{\infty} \frac{1}{n^{4}}$$ 
Sum(1/(n^4), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{1}{n^{4}}$$
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
$$a_{n} = \frac{1}{n^{4}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\left(n + 1\right)^{4}}{n^{4}}\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
  4
pi 
---
 90
$$\frac{\pi^{4}}{90}$$ 
pi^4/90
Numerical answer [src] 
1.08232323371113819151600369654
1.08232323371113819151600369654
The graph
Sum of series 1/n^4

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