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  • Sum of series:
  • k^2*x-12*k^14-2*x
  • (1)/(2^n+n) (1)/(2^n+n)
  • nx^n
  • 1/((1+r)^n)

  • Identical expressions

  • k^ two *x- twelve *k^ fourteen - two *x
  • k squared multiply by x minus 12 multiply by k to the power of 14 minus 2 multiply by x
  • k to the power of two multiply by x minus twelve multiply by k to the power of fourteen minus two multiply by x
  • k2*x-12*k14-2*x
  • k²*x-12*k^14-2*x
  • k to the power of 2*x-12*k to the power of 14-2*x
  • k^2x-12k^14-2x
  • k2x-12k14-2x

  • Similar expressions

  • k^2*x+12*k^14-2*x
  • k^2*x-12*k^14+2*x
Sum of series/ k^2*x-12*k^14-2*x

Sum of series k^2*x-12*k^14-2*x


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The solution

You have entered [src] 
  oo                       
 ___                       
 \  `                      
  \   / 2         14      \
  /   \k *x - 12*k   - 2*x/
 /__,                      
n = 1
$$\sum_{n=1}^{\infty} \left(- 2 x + \left(- 12 k^{14} + k^{2} x\right)\right)$$ 
Sum(k^2*x - 12*k^14 - 2*x, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$- 2 x + \left(- 12 k^{14} + k^{2} x\right)$$
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
$$a_{n} = - 12 k^{14} + k^{2} x - 2 x$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} 1$$
Let's take the limit
we find
True

False
The answer [src] 
   /      14            2\
oo*\- 12*k   - 2*x + x*k /
$$\infty \left(- 12 k^{14} + k^{2} x - 2 x\right)$$ 
oo*(-12*k^14 - 2*x + x*k^2)

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