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Sum of series (2+3sqrtn)/(2n-5)

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  oo             
____             
\   `            
 \            ___
  \   2 + 3*\/ n 
  /   -----------
 /      2*n - 5  
/___,            
n = 1

\sum_{n=1}^{\infty} \frac{3 \sqrt{n} + 2}{2 n - 5}

Sum((2 + 3*sqrt(n))/(2*n - 5), (n, 1, oo))

The radius of convergence of the power series

Given number:

\frac{3 \sqrt{n} + 2}{2 n - 5}

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{3 \sqrt{n} + 2}{2 n - 5}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty}\left(\frac{\left(3 \sqrt{n} + 2\right) \left|{\frac{2 n - 3}{2 n - 5}}\right|}{3 \sqrt{n + 1} + 2}\right)

True

False

The rate of convergence of the power series

The graph