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Sum of series/ cos2n

Sum of series cos2n

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  oo          
 __           
 \ `          
  )   cos(2*n)
 /_,          
n = 1

\sum_{n=1}^{\infty} \cos{\left(2 n \right)}

Sum(cos(2*n), (n, 1, oo))

The radius of convergence of the power series

Given number:

\cos{\left(2 n \right)}

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} = \cos{\left(2 n \right)}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty} \left|{\frac{\cos{\left(2 n \right)}}{\cos{\left(2 n + 2 \right)}}}\right|

1 = \lim_{n \to \infty} \left|{\frac{\cos{\left(2 n \right)}}{\cos{\left(2 n + 2 \right)}}}\right|

False

The rate of convergence of the power series

Numerical answer

The series diverges

The graph