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Sum of series:
1/n^1,5
2^(2*n-1)/9^n
(x^n)/(n*(n+1))
1/(2n+1)*2^2n+1
Identical expressions
two *(x- six)^ two
2 multiply by (x minus 6) squared
two multiply by (x minus six) to the power of two
2*(x-6)2
2*x-62
2*(x-6)²
2*(x-6) to the power of 2
2(x-6)^2
2(x-6)2
2x-62
2x-6^2
Similar expressions
2*(x+6)^2

Sum of series 2*(x-6)^2

The solution

You have entered [src]

  oo            
 ___            
 \  `           
  \            2
  /   2*(x - 6) 
 /__,           
n = 1

$$\sum_{n=1}^{\infty} 2 \left(x - 6\right)^{2}$$

Sum(2*(x - 6)^2, (n, 1, oo))

The radius of convergence of the power series

Given number:
$$2 \left(x - 6\right)^{2}$$
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
$$a_{n} = 2 \left(x - 6\right)^{2}$$
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]

           2
oo*(-6 + x)

$$\infty \left(x - 6\right)^{2}$$

oo*(-6 + x)^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 2*(x-6)^2

The solution

Examples of finding the sum of a series