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k^2-k

  • How to use it?

  • Sum of series:
  • 1/n! 1/n!
  • 1/(2^n) 1/(2^n)
  • 2/n 2/n
  • cos(n)*x/n^2

  • Identical expressions

  • k^ two -k
  • k squared minus k
  • k to the power of two minus k
  • k2-k
  • k²-k
  • k to the power of 2-k

  • Similar expressions

  • k^2+k
Sum of series/ k^2-k

Sum of series k^2-k


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The solution

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

False
The rate of convergence of the power series
Numerical answer
The series diverges
The graph
Sum of series k^2-k

    Examples of finding the sum of a series

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