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tg^2×(1/n)

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  • Sum of series:
  • 7x²
  • 10*60*0,18 10*60*0,18
  • tg^2×(1/n) tg^2×(1/n)
  • nln(n)/e^n nln(n)/e^n

  • Identical expressions

  • tg^ two ×(one /n)
  • tg squared ×(1 divide by n)
  • tg to the power of two ×(one divide by n)
  • tg2×(1/n)
  • tg2×1/n
  • tg²×(1/n)
  • tg to the power of 2×(1/n)
  • tg^2×1/n
  • tg^2×(1 divide by n)
Sum of series/ tg^2×(1/n)

Sum of series tg^2×(1/n)


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The solution

You have entered [src] 
  oo         
 ___         
 \  `        
  \      2/1\
   )  tan |-|
  /       \n/
 /__,        
n = 1
$$\sum_{n=1}^{\infty} \tan^{2}{\left(\frac{1}{n} \right)}$$ 
Sum(tan(1/n)^2, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\tan^{2}{\left(\frac{1}{n} \right)}$$
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
$$a_{n} = \tan^{2}{\left(\frac{1}{n} \right)}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\tan^{2}{\left(\frac{1}{n} \right)} \left|{\frac{1}{\tan^{2}{\left(\frac{1}{n + 1} \right)}}}\right|\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The graph
Sum of series tg^2×(1/n)

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