Sum of series arccot(x)

You have entered [src]

  oo         
 __          
 \ `         
  )   acot(x)
 /_,         
n = 1

\sum_{n=1}^{\infty} \operatorname{acot}{\left(x \right)}

Sum(acot(x), (n, 1, oo))

The radius of convergence of the power series

Given number:

\operatorname{acot}{\left(x \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} = \operatorname{acot}{\left(x \right)}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty} 1

True

False

The answer [src]

oo*acot(x)

\infty \operatorname{acot}{\left(x \right)}

oo*acot(x)