Mister Exam

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Sum of series:
5^n
2(1/(n^2+5n+6))
1/(1+n^2)
(n^3+n+5)/(n+6)
Identical expressions
twenty-four /((five -3n)(two -3n))
24 divide by ((5 minus 3n)(2 minus 3n))
twenty minus four divide by ((five minus 3n)(two minus 3n))
24/5-3n2-3n
24 divide by ((5-3n)(2-3n))
Similar expressions
24/((5-3n)(2+3n))
24/((5-3n)*(2-3n))
24/((5+3n)(2-3n))

Sum of series/ 24/((5-3n)(2-3n))

Sum of series 24/((5-3n)(2-3n))

The solution

You have entered [src]

  oo                     
 ___                     
 \  `                    
  \            24        
   )  -------------------
  /   (5 - 3*n)*(2 - 3*n)
 /__,                    
n = 4

\sum_{n=4}^{\infty} \frac{24}{\left(2 - 3 n\right) \left(5 - 3 n\right)}

Sum(24/(((5 - 3*n)*(2 - 3*n))), (n, 4, oo))

The radius of convergence of the power series

Given number:

\frac{24}{\left(2 - 3 n\right) \left(5 - 3 n\right)}

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{24}{\left(2 - 3 n\right) \left(5 - 3 n\right)}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty}\left(\left(3 n + 1\right) \left|{\frac{1}{3 n - 5}}\right|\right)

Let's take the limit
we find

True

False

The rate of convergence of the power series

The answer [src]

12*Gamma(13/3)
--------------
35*Gamma(10/3)

\frac{12 \Gamma\left(\frac{13}{3}\right)}{35 \Gamma\left(\frac{10}{3}\right)}

12*gamma(13/3)/(35*gamma(10/3))

Numerical answer [src]

1.14285714285714285714285714286

1.14285714285714285714285714286

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 24/((5-3n)(2-3n))

The solution

Examples of finding the sum of a series