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(-1)^nsin(1/n)

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  • Sum of series:
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  • 1/(n*ln(n)) 1/(n*ln(n))
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  • arccot(x)

  • Identical expressions

  • (- one)^nsin(one /n)
  • ( minus 1) to the power of n sinus of (1 divide by n)
  • ( minus one) to the power of n sinus of (one divide by n)
  • (-1)nsin(1/n)
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  • -1^nsin1/n
  • (-1)^nsin(1 divide by n)

  • Similar expressions

  • (1)^nsin(1/n)
Sum of series/ (-1)^nsin(1/n)

Sum of series (-1)^nsin(1/n)


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The solution

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

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