Mister Exam

Lang:

Sum of series/ (x-7)^3

Sum of series (x-7)^3

You have entered [src]

  oo          
 ___          
 \  `         
  \          3
  /   (x - 7) 
 /__,         
x = 1

\sum_{x=1}^{\infty} \left(x - 7\right)^{3}

Sum((x - 7)^3, (x, 1, oo))

The radius of convergence of the power series

Given number:

\left(x - 7\right)^{3}

It is a series of species

a_{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:

R^{d} = \frac{x_{0} + \lim_{x \to \infty} \left|{\frac{a_{x}}{a_{x + 1}}}\right|}{c}

In this case

a_{x} = \left(x - 7\right)^{3}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{x \to \infty}\left(\left(x - 7\right)^{2} \left|{x - 7}\right| \left|{\frac{1}{\left(x - 6\right)^{3}}}\right|\right)

True

False

The rate of convergence of the power series

Numerical answer

The series diverges

The graph