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Sum of series/ (n*a+b)/((2*a))

Sum of series (n*a+b)/((2*a))


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The solution

You have entered [src] 
  oo         
 ___         
 \  `        
  \   n*a + b
   )  -------
  /     2*a  
 /__,        
n = 1
$$\sum_{n=1}^{\infty} \frac{a n + b}{2 a}$$ 
Sum((n*a + b)/((2*a)), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{a n + b}{2 a}$$
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
$$a_{n} = \frac{a n + b}{2 a}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} \left|{\frac{a n + b}{a \left(n + 1\right) + b}}\right|$$
Let's take the limit
we find
True

False
The answer [src] 
     oo*b
oo + ----
      a
$$\infty + \frac{\infty b}{a}$$ 
oo + oo*b/a

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