Mister Exam

Other calculators

Sum of series/ 2/(9x^2+21x-8)

Sum of series 2/(9x^2+21x-8)


∑
=

The solution

You have entered [src] 
  oo                 
____                 
\   `                
 \           2       
  \   ---------------
  /      2           
 /    9*x  + 21*x - 8
/___,                
n = 1
$$\sum_{n=1}^{\infty} \frac{2}{\left(9 x^{2} + 21 x\right) - 8}$$ 
Sum(2/(9*x^2 + 21*x - 8), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{2}{\left(9 x^{2} + 21 x\right) - 8}$$
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
$$a_{n} = \frac{2}{9 x^{2} + 21 x - 8}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(2 \left|{\frac{\frac{9 x^{2}}{2} + \frac{21 x}{2} - 4}{9 x^{2} + 21 x - 8}}\right|\right)$$
Let's take the limit
we find
$$1 = 2 \left|{\frac{\frac{9 x^{2}}{2} + \frac{21 x}{2} - 4}{9 x^{2} + 21 x - 8}}\right|$$
$$1 = 2 \left|{\frac{\frac{9 x^{2}}{2} + \frac{21 x}{2} - 4}{9 x^{2} + 21 x - 8}}\right|$$
False
The answer [src] 
       oo       
----------------
        2       
-8 + 9*x  + 21*x
$$\frac{\infty}{9 x^{2} + 21 x - 8}$$ 
oo/(-8 + 9*x^2 + 21*x)

    Examples of finding the sum of a series

    © Mister Exam – Calculator