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Sum of series:
6/9n^2+12n-5
1/(3n+1)(3n+4)
7^x/(5^x-3)
38
Identical expressions
six /9n^ two +12n- five
6 divide by 9n squared plus 12n minus 5
six divide by 9n to the power of two plus 12n minus five
6/9n2+12n-5
6/9n²+12n-5
6/9n to the power of 2+12n-5
6 divide by 9n^2+12n-5
Similar expressions
6/9n^2+12n+5
6/9n^2-12n-5

Sum of series/ 6/9n^2+12n-5

Sum of series 6/9n^2+12n-5

The solution

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  oo                   
____                   
\   `                  
 \    /   2           \
  \   |2*n            |
  /   |---- + 12*n - 5|
 /    \ 3             /
/___,                  
n = 1

\sum_{n=1}^{\infty} \left(\left(\frac{2 n^{2}}{3} + 12 n\right) - 5\right)

Sum(2*n^2/3 + 12*n - 5, (n, 1, oo))

The radius of convergence of the power series

Given number:

\left(\frac{2 n^{2}}{3} + 12 n\right) - 5

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{2 n^{2}}{3} + 12 n - 5

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty}\left(\frac{\left|{\frac{2 n^{2}}{3} + 12 n - 5}\right|}{12 n + \frac{2 \left(n + 1\right)^{2}}{3} + 7}\right)

Let's take the limit
we find

True

False

The rate of convergence of the power series

Numerical answer

The series diverges

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 6/9n^2+12n-5

The solution

Examples of finding the sum of a series