Mister Exam

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Sum of series:
2i+1
5000n+60000
1/(n^2-3n+2)
sin(n*x)/(n^2+1)
Identical expressions
one /(n^ two -3n+ two)
1 divide by (n squared minus 3n plus 2)
one divide by (n to the power of two minus 3n plus two)
1/(n2-3n+2)
1/n2-3n+2
1/(n²-3n+2)
1/(n to the power of 2-3n+2)
1/n^2-3n+2
1 divide by (n^2-3n+2)
Similar expressions
1/(n^2-3n-2)
1/(n^2+3n+2)

Sum of series/ 1/(n^2-3n+2)

Sum of series 1/(n^2-3n+2)

The solution

You have entered [src]

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

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

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

The radius of convergence of the power series

Given number:

\frac{1}{\left(n^{2} - 3 n\right) + 2}

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^{2} - 3 n + 2}

and

x_{0} = 0

d = 0

c = 1

then

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

Let's take the limit
we find

True

False

The rate of convergence of the power series

The answer [src]

nan

\text{NaN}

nan

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 1/(n^2-3n+2)

The solution

Examples of finding the sum of a series