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sin1/(n^2)

  • How to use it?

  • Sum of series:
  • 1/(n(n+2)) 1/(n(n+2))
  • (5/6)^n (5/6)^n
  • n*2^n n*2^n
  • sin1/(n^2) sin1/(n^2)

  • Identical expressions

  • sin1/(n^ two)
  • sinus of 1 divide by (n squared )
  • sinus of 1 divide by (n to the power of two)
  • sin1/(n2)
  • sin1/n2
  • sin1/(n²)
  • sin1/(n to the power of 2)
  • sin1/n^2
  • sin1 divide by (n^2)
Sum of series/ sin1/(n^2)

Sum of series sin1/(n^2)


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The solution

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

False
The rate of convergence of the power series
The answer [src] 
  2       
pi *sin(1)
----------
    6
$$\frac{\pi^{2} \sin{\left(1 \right)}}{6}$$ 
pi^2*sin(1)/6
Numerical answer [src] 
1.38416428917483536443363254700
1.38416428917483536443363254700
The graph
Sum of series sin1/(n^2)

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