Mister Exam

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Sum of series:
1/n^x
n^2*x^n/4^n
factorial(2*n)/sqrt(2^n+5)
36n/(7^n)
Identical expressions
36n/(seven ^n)
36n divide by (7 to the power of n)
36n divide by (seven to the power of n)
36n/(7n)
36n/7n
36n/7^n
36n divide by (7^n)

Sum of series/ 36n/(7^n)

Sum of series 36n/(7^n)

The solution

You have entered [src]

  oo      
____      
\   `     
 \    36*n
  \   ----
  /     n 
 /     7  
/___,     
n = 1

$$\sum_{n=1}^{\infty} \frac{36 n}{7^{n}}$$

Sum((36*n)/7^n, (n, 1, oo))

The radius of convergence of the power series

Given number:
$$\frac{36 n}{7^{n}}$$
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
$$a_{n} = 36 n$$
and
$$x_{0} = -7$$
,
$$d = -1$$
,
$$c = 0$$
then
$$\frac{1}{R} = \tilde{\infty} \left(-7 + \lim_{n \to \infty}\left(\frac{36 n}{36 n + 36}\right)\right)$$
Let's take the limit
we find

False

$$R = 0$$

The rate of convergence of the power series

The answer [src]

$$7$$

Numerical answer [src]

7.00000000000000000000000000000

7.00000000000000000000000000000

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 36n/(7^n)

The solution

Examples of finding the sum of a series