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n/1+n^2
Sum of series/ n/1+n^2

Sum of series n/1+n^2


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The solution

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

False
The rate of convergence of the power series
The answer [src] 
oo
$$\infty$$ 
oo
Numerical answer
The series diverges
The graph
Sum of series n/1+n^2

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