Mister Exam

Sum of series sin1/n



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The solution

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

False
The rate of convergence of the power series
The answer [src]
oo
$$\infty$$
oo
Numerical answer [src]
0.e+2
0.e+2
The graph
Sum of series sin1/n

    Examples of finding the sum of a series