Mister Exam

Other calculators

(x-6)^2
Sum of series/ (x-6)^2

Sum of series (x-6)^2


∑
=

The solution

You have entered [src] 
  oo           
 ___           
 \  `          
  \           2
  /    (x - 6) 
 /__,          
x = 11
∑x=11∞(x−6)2\sum_{x=11}^{\infty} \left(x - 6\right)^{2} 
Sum((x - 6)^2, (x, 11, oo))
The radius of convergence of the power series
Given number:
(x−6)2\left(x - 6\right)^{2}
It is a series of species
ax(cx−x0)dxa_{x} \left(c x - x_{0}\right)^{d x}
- power series.
The radius of convergence of a power series can be calculated by the formula:
Rd=x0+lim⁡x→∞∣axax+1∣cR^{d} = \frac{x_{0} + \lim_{x \to \infty} \left|{\frac{a_{x}}{a_{x + 1}}}\right|}{c}
In this case
ax=(x−6)2a_{x} = \left(x - 6\right)^{2}
and
x0=0x_{0} = 0
,
d=0d = 0
,
c=1c = 1
then
1=lim⁡x→∞((x−6)2∣1(x−5)2∣)1 = \lim_{x \to \infty}\left(\left(x - 6\right)^{2} \left|{\frac{1}{\left(x - 5\right)^{2}}}\right|\right)
Let's take the limit
we find
True

False
The rate of convergence of the power series
11.017.011.512.012.513.013.514.014.515.015.516.016.50500
The answer [src] 
oo
∞\infty 
oo
Numerical answer
The series diverges
The graph
Sum of series (x-6)^2

    Examples of finding the sum of a series

    © Mister Exam – Calculator