Mister Exam

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Sum of series:
1/((3*n+1)*(3*n+4))
log((n^2+1)/n^2)
arcsin(1/sqrt(n))
2^n+1(n^3+1)/(n+1)!
Graphing y =:
1/(1-x^2)
Limit of the function:
1/(1-x^2)
Derivative of:
1/(1-x^2)
Identical expressions
one /(one -x^ two)
1 divide by (1 minus x squared )
one divide by (one minus x to the power of two)
1/(1-x2)
1/1-x2
1/(1-x²)
1/(1-x to the power of 2)
1/1-x^2
1 divide by (1-x^2)
Similar expressions
1/(1+x^2)

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

The solution

You have entered [src]

  oo        
____        
\   `       
 \      1   
  \   ------
  /        2
 /    1 - x 
/___,       
n = 1

$$\sum_{n=1}^{\infty} \frac{1}{1 - x^{2}}$$

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

The radius of convergence of the power series

Given number:
$$\frac{1}{1 - x^{2}}$$
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
$$a_{n} = \frac{1}{1 - x^{2}}$$
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 - x

$$\frac{\infty}{1 - x^{2}}$$

oo/(1 - 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 1/(1-x^2)

The solution

Examples of finding the sum of a series