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tg(1/n^(1/2))

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  • Sum of series:
  • tg(1/n^(1/2)) tg(1/n^(1/2))
  • -16 -16
  • x(x+1)
  • arctg(x^3)/(n(n+2)(n+3))

  • Identical expressions

  • tg(one /n^(one / two))
  • tg(1 divide by n to the power of (1 divide by 2))
  • tg(one divide by n to the power of (one divide by two))
  • tg(1/n(1/2))
  • tg1/n1/2
  • tg1/n^1/2
  • tg(1 divide by n^(1 divide by 2))
Sum of series/ tg(1/n^(1/2))

Sum of series tg(1/n^(1/2))


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The solution

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

False
The rate of convergence of the power series
The answer [src] 
  oo            
____            
\   `           
 \       /  1  \
  \   tan|-----|
  /      |  ___|
 /       \\/ n /
/___,           
n = 1
$$\sum_{n=1}^{\infty} \tan{\left(\frac{1}{\sqrt{n}} \right)}$$ 
Sum(tan(1/sqrt(n)), (n, 1, oo))
The graph
Sum of series tg(1/n^(1/2))

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