Mister Exam

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Sum of series:
1/(n*lnn)
(x-2)^2
ln^n(x)/n!
n^2/2^n
Derivative of:
(x-2)^2
Integral of d{x}:
(x-2)^2
Graphing y =:
(x-2)^2
Identical expressions
(x- two)^ two
(x minus 2) squared
(x minus two) to the power of two
(x-2)2
x-22
(x-2)²
(x-2) to the power of 2
x-2^2
Similar expressions
(x+2)^2

Sum of series/ (x-2)^2

Sum of series (x-2)^2

The solution

You have entered [src]

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

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

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

The radius of convergence of the power series

Given number:

\left(x - 2\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} = \left(x - 2\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*(-2 + x)

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

oo*(-2 + 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
```