Mister Exam

# Sum of series cos(xi+yi)

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### The solution

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  oo
__
\
)   cos(x*I + y*I)
/_,
n = 1               
$$\sum_{n=1}^{\infty} \cos{\left(i x + i y \right)}$$
Sum(cos(x*i + y*i), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\cos{\left(i x + i y \right)}$$
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
$$a_{n} = \cosh{\left(x + y \right)}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} 1$$
Let's take the limit
we find
True

False
oo*cosh(x + y)
$$\infty \cosh{\left(x + y \right)}$$
oo*cosh(x + y)`