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  • Sum of series:
  • sin(x)/n
  • sen(na)
  • log(1+3/n) log(1+3/n)
  • ln(1+3/n) ln(1+3/n)

  • Identical expressions

  • (one /n)*sin(x/n)
  • (1 divide by n) multiply by sinus of (x divide by n)
  • (one divide by n) multiply by sinus of (x divide by n)
  • (1/n)sin(x/n)
  • 1/nsinx/n
  • (1 divide by n)*sin(x divide by n)
Sum of series/ (1/n)*sin(x/n)

Sum of series (1/n)*sin(x/n)


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The solution

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

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