Mister Exam

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Sum of series:
6/((3n-2)(3n+4))
(7^n-2^n)/14^n
(n-1)/2^(n+1)
6/(n^2-10n+24)
Identical expressions
six /(n^ two -10n+ twenty-four)
6 divide by (n squared minus 10n plus 24)
six divide by (n to the power of two minus 10n plus twenty minus four)
6/(n2-10n+24)
6/n2-10n+24
6/(n²-10n+24)
6/(n to the power of 2-10n+24)
6/n^2-10n+24
6 divide by (n^2-10n+24)
Similar expressions
6/(n^2-10n-24)
6/(n^2+10n+24)

Sum of series/ 6/(n^2-10n+24)

Sum of series 6/(n^2-10n+24)

The solution

You have entered [src]

  oo                
____                
\   `               
 \          6       
  \   --------------
  /    2            
 /    n  - 10*n + 24
/___,               
n = 7

\sum_{n=7}^{\infty} \frac{6}{\left(n^{2} - 10 n\right) + 24}

Sum(6/(n^2 - 10*n + 24), (n, 7, oo))

The radius of convergence of the power series

Given number:

\frac{6}{\left(n^{2} - 10 n\right) + 24}

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{6}{n^{2} - 10 n + 24}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty}\left(6 \left|{\frac{- \frac{5 n}{3} + \frac{\left(n + 1\right)^{2}}{6} + \frac{7}{3}}{n^{2} - 10 n + 24}}\right|\right)

Let's take the limit
we find

True

False

The rate of convergence of the power series

The answer [src]

9/2

\frac{9}{2}

9/2

Numerical answer [src]

4.50000000000000000000000000000

4.50000000000000000000000000000

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
```

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Identical expressions

Similar expressions

Sum of series 6/(n^2-10n+24)

The solution

Examples of finding the sum of a series