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1/(r+1)

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  • Sum of series:
  • 1/(r+1) 1/(r+1)
  • -2 -2
  • log(n/2^i)
  • 5/3^n 5/3^n

  • Identical expressions

  • one /(r+ one)
  • 1 divide by (r plus 1)
  • one divide by (r plus one)
  • 1/r+1
  • 1 divide by (r+1)

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  • 1/(r-1)
Sum of series/ 1/(r+1)

Sum of series 1/(r+1)


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The solution

You have entered [src] 
  oo       
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 \  `      
  \     1  
   )  -----
  /   r + 1
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r = 1
$$\sum_{r=1}^{\infty} \frac{1}{r + 1}$$ 
Sum(1/(r + 1), (r, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{1}{r + 1}$$
It is a series of species
$$a_{r} \left(c x - x_{0}\right)^{d r}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{r \to \infty} \left|{\frac{a_{r}}{a_{r + 1}}}\right|}{c}$$
In this case
$$a_{r} = \frac{1}{r + 1}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{r \to \infty}\left(\frac{r + 2}{r + 1}\right)$$
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 1/(r+1)

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