Mister Exam

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Sum of series:
6/(n^2-10n+24)
x^n/sqrt(n+1)
(n^2)(tg(pi/2)^5)
(2x-4)
Identical expressions
(n^ two)(tg(pi/ two)^ five)
(n squared )(tg( Pi divide by 2) to the power of 5)
(n to the power of two)(tg( Pi divide by two) to the power of five)
(n2)(tg(pi/2)5)
n2tgpi/25
(n²)(tg(pi/2)⁵)
(n to the power of 2)(tg(pi/2) to the power of 5)
n^2tgpi/2^5
(n^2)(tg(pi divide by 2)^5)

Sum of series/ (n^2)(tg(pi/2)^5)

Sum of series (n^2)(tg(pi/2)^5)

The solution

You have entered [src]

  oo             
 ___             
 \  `            
  \    2    5/pi\
   )  n *tan |--|
  /          \2 /
 /__,            
n = 1

$$\sum_{n=1}^{\infty} n^{2} \tan^{5}{\left(\frac{\pi}{2} \right)}$$

Sum(n^2*tan(pi/2)^5, (n, 1, oo))

The radius of convergence of the power series

Given number:
$$n^{2} \tan^{5}{\left(\frac{\pi}{2} \right)}$$
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
$$a_{n} = \tilde{\infty} n^{2}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} \text{NaN}$$
Let's take the limit
we find

False

False

The rate of convergence of the power series

The answer [src]

zoo

$$\tilde{\infty}$$

±oo

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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How to use it?

Identical expressions

Sum of series (n^2)(tg(pi/2)^5)

The solution

Examples of finding the sum of a series