Mister Exam

Lang:

Other calculators

How to use it?
Sum of series:
1/(n(n+1))
e^n/n^10
((2*n+4)/(5*n+7))^n*x^n
2^2
Identical expressions
e^n/n^ ten
e to the power of n divide by n to the power of 10
e to the power of n divide by n to the power of ten
en/n10
e^n divide by n^10

Sum of series/ e^n/n^10

Sum of series e^n/n^10

The solution

You have entered [src]

  oo     
____     
\   `    
 \      n
  \    E 
   )  ---
  /    10
 /    n  
/___,    
n = 1

$$\sum_{n=1}^{\infty} \frac{e^{n}}{n^{10}}$$

Sum(E^n/n^10, (n, 1, oo))

The radius of convergence of the power series

Given number:
$$\frac{e^{n}}{n^{10}}$$
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
$$a_{n} = \frac{1}{n^{10}}$$
and
$$x_{0} = - e$$
,
$$d = 1$$
,
$$c = 0$$
then
$$R = \tilde{\infty} \left(- e + \lim_{n \to \infty}\left(\frac{\left(n + 1\right)^{10}}{n^{10}}\right)\right)$$
Let's take the limit
we find

False

The rate of convergence of the power series

The answer [src]

oo

$$\infty$$

oo

The graph

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^n/n^10

The solution

Examples of finding the sum of a series