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1/(2*n-1)^4

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  • Sum of series:
  • pi pi
  • 4x
  • 1/(2*n-1)^4 1/(2*n-1)^4
  • 1/4^n 1/4^n

  • Identical expressions

  • one /(two *n- one)^ four
  • 1 divide by (2 multiply by n minus 1) to the power of 4
  • one divide by (two multiply by n minus one) to the power of four
  • 1/(2*n-1)4
  • 1/2*n-14
  • 1/(2*n-1)⁴
  • 1/(2n-1)^4
  • 1/(2n-1)4
  • 1/2n-14
  • 1/2n-1^4
  • 1 divide by (2*n-1)^4

  • Similar expressions

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

Sum of series 1/(2*n-1)^4


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The solution

You have entered [src] 
  oo            
____            
\   `           
 \        1     
  \   ----------
  /            4
 /    (2*n - 1) 
/___,           
n = 1
$$\sum_{n=1}^{\infty} \frac{1}{\left(2 n - 1\right)^{4}}$$ 
Sum(1/((2*n - 1)^4), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{1}{\left(2 n - 1\right)^{4}}$$
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
$$a_{n} = \frac{1}{\left(2 n - 1\right)^{4}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\left(2 n + 1\right)^{4} \left|{\frac{1}{\left(2 n - 1\right)^{4}}}\right|\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
  4
pi 
---
 96
$$\frac{\pi^{4}}{96}$$ 
pi^4/96
Numerical answer [src] 
1.01467803160419205454625346551
1.01467803160419205454625346551
The graph
Sum of series 1/(2*n-1)^4

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