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

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


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The solution

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

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