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Sum of series:
3/(n(n+2))
sin1/n
ln(n+1)/n
((n+1)^n*3^(2n-1))/(2n+1)!
Identical expressions
one /(two k- one)^2
1 divide by (2k minus 1) squared
one divide by (two k minus one) squared
1/(2k-1)2
1/2k-12
1/(2k-1)²
1/(2k-1) to the power of 2
1/2k-1^2
1 divide by (2k-1)^2
Similar expressions
1/(2k+1)^2

Sum of series 1/(2k-1)^2

The solution

You have entered [src]

  oo            
____            
\   `           
 \        1     
  \   ----------
  /            2
 /    (2*k - 1) 
/___,           
n = 1

$$\sum_{n=1}^{\infty} \frac{1}{\left(2 k - 1\right)^{2}}$$

Sum(1/((2*k - 1)^2), (n, 1, oo))

The radius of convergence of the power series

Given number:
$$\frac{1}{\left(2 k - 1\right)^{2}}$$
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
$$a_{n} = \frac{1}{\left(2 k - 1\right)^{2}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} 1$$
Let's take the limit
we find

True

False

The answer [src]

     oo    
-----------
          2
(-1 + 2*k)

$$\frac{\infty}{\left(2 k - 1\right)^{2}}$$

oo/(-1 + 2*k)^2

Examples of finding the sum of a series

The Sum of the Power Series
```
x^n/n
```
```
(x-1)^n
```
Factorial
```
1/2^(n!)
```
```
n^2/n!
```
```
x^n/n!
```
```
k!/(n!*(n+k)!)
```
Flint Hills Series
```
csc(n)^2/n^3
```
Basel problem
```
1/n^2
```
```
1/n^4
```
```
1/n^6
```
Harmonic series
```
1/n
```
Grandi's series
```
(-1)^n
```
Alternating series
```
(-1)^(n + 1)/n
```
```
(n + 2)*(-1)^(n - 1)
```
```
(3*n - 1)/(-5)^n
```
```
(-1)^(n - 1)*n/(6*n - 5)
```
Newton–Mercator series
```
(-1)^(n + 1)/n*x^n
```
Exam the series for convergence
```
(3*n - 1)/(-5)^n
```

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Identical expressions

Similar expressions

Sum of series 1/(2k-1)^2

The solution

Examples of finding the sum of a series