Sum of series nsinn

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

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

Sum(n*sin(n), (n, 1, oo))

The radius of convergence of the power series

Given number:

n \sin{\left(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} = n \sin{\left(n \right)}

and

x_{0} = 0

d = 0

c = 1

then

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

True

False

The rate of convergence of the power series

Numerical answer

The series diverges

The graph