Mister Exam

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Sum of series:
24/(9n^2-12n-5)
n^(2/3)*arctg(1/n^2)
2/(n^2+6n+8)
tan(n*x)
Derivative of:
a^2
Canonical form:
a^2
Limit of the function:
a^2
Identical expressions
a^ two
a squared
a to the power of two
a2
a²
a to the power of 2

Sum of series/ a^2

Sum of series a^2

The solution

You have entered [src]

  oo    
 ___    
 \  `   
  \    2
  /   a 
 /__,   
n = 1

$$\sum_{n=1}^{\infty} a^{2}$$

Sum(a^2, (n, 1, oo))

The radius of convergence of the power series

Given number:
$$a^{2}$$
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
$$a_{n} = a^{2}$$
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*a

$$\infty a^{2}$$

oo*a^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
```

Other calculators

How to use it?

Identical expressions

Sum of series a^2

The solution

Examples of finding the sum of a series