Mister Exam

Other calculators

(1/n)*sin(1/n)

  • How to use it?

  • Sum of series:
  • 6/9n^2+12n-5 6/9n^2+12n-5
  • 5^n 5^n
  • n^n/2^(n+1) n^n/2^(n+1)
  • n^3 n^3

  • Identical expressions

  • (one /n)*sin(one /n)
  • (1 divide by n) multiply by sinus of (1 divide by n)
  • (one divide by n) multiply by sinus of (one divide by n)
  • (1/n)sin(1/n)
  • 1/nsin1/n
  • (1 divide by n)*sin(1 divide by n)

  • Similar expressions

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

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


∑
=

The solution

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

False
The rate of convergence of the power series
Numerical answer [src] 
1.47282823195618529629494738382
1.47282823195618529629494738382
The graph
Sum of series (1/n)*sin(1/n)

    Examples of finding the sum of a series

    © Mister Exam – Calculator