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  • Sum of series:
  • x^(2*n)
  • 1^n/(1+n^2) 1^n/(1+n^2)
  • sqrt(9)*3 sqrt(9)*3
  • sen(5n)/k^2

  • Identical expressions

  • sen(5n)/k^ two
  • sen(5n) divide by k squared
  • sen(5n) divide by k to the power of two
  • sen(5n)/k2
  • sen5n/k2
  • sen(5n)/k²
  • sen(5n)/k to the power of 2
  • sen5n/k^2
  • sen(5n) divide by k^2
Sum of series/ sen(5n)/k^2

Sum of series sen(5n)/k^2


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The solution

You have entered [src] 
  oo          
____          
\   `         
 \    sin(5*n)
  \   --------
  /       2   
 /       k    
/___,         
n = 1
$$\sum_{n=1}^{\infty} \frac{\sin{\left(5 n \right)}}{k^{2}}$$ 
Sum(sin(5*n)/k^2, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{\sin{\left(5 n \right)}}{k^{2}}$$
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
$$a_{n} = \frac{\sin{\left(5 n \right)}}{k^{2}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} \left|{\frac{\sin{\left(5 n \right)}}{\sin{\left(5 n + 5 \right)}}}\right|$$
Let's take the limit
we find
$$1 = \lim_{n \to \infty} \left|{\frac{\sin{\left(5 n \right)}}{\sin{\left(5 n + 5 \right)}}}\right|$$
False

    Examples of finding the sum of a series

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