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Sum of series/ (w+1)/w

Sum of series (w+1)/w


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The solution

You have entered [src] 
  oo       
 ___       
 \  `      
  \   w + 1
   )  -----
  /     w  
 /__,      
y = 1
$$\sum_{y=1}^{\infty} \frac{w + 1}{w}$$ 
Sum((w + 1)/w, (y, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{w + 1}{w}$$
It is a series of species
$$a_{y} \left(c y - y_{0}\right)^{d y}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{y_{0} + \lim_{y \to \infty} \left|{\frac{a_{y}}{a_{y + 1}}}\right|}{c}$$
In this case
$$a_{y} = \frac{w + 1}{w}$$
and
$$y_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{y \to \infty} 1$$
Let's take the limit
we find
True

False
The answer [src] 
oo*(1 + w)
----------
    w
$$\frac{\infty \left(w + 1\right)}{w}$$ 
oo*(1 + w)/w

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