Mister Exam

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Sum of series:
(8/((2*n+1)*(2*n+1)*3.1416*3.1416))*exp(-(2*n+1)*0.197*3.1416*3.1416*0.25)
sinn
factorial(n)/(n^3+n+8)
1/((2n-1)*(2n+5))
Integral of d{x}:
e^(a*x)
Derivative of:
e^(a*x)
Limit of the function:
e^(a*x)
Identical expressions
e^(a*x)
e to the power of (a multiply by x)
e(a*x)
ea*x
e^(ax)
e(ax)
eax
e^ax

Sum of series e^(a*x)

The solution

You have entered [src]

  oo      
 ___      
 \  `     
  \    a*x
  /   E   
 /__,     
n = 0

$$\sum_{n=0}^{\infty} e^{a x}$$

Sum(E^(a*x), (n, 0, oo))

The radius of convergence of the power series

Given number:
$$e^{a x}$$
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
$$a_{n} = e^{a x}$$
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]

    a*x
oo*e

$$\infty e^{a x}$$

oo*exp(a*x)

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 e^(a*x)

The solution

Examples of finding the sum of a series