Mister Exam

### Other calculators

• #### How to use it?

• Sum of series:
• (2/9)^n
• n^2/n!
• (2/3)^n
• (-1)^(n+1)/n
• #### Identical expressions

• (two / nine)^n
• (2 divide by 9) to the power of n
• (two divide by nine) to the power of n
• (2/9)n
• 2/9n
• 2/9^n
• (2 divide by 9)^n

# Sum of series (2/9)^n

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### The solution

You have entered [src]
  oo
___
\
\      n
/   2/9
/__,
n = 1     
$$\sum_{n=1}^{\infty} \left(\frac{2}{9}\right)^{n}$$
Sum((2/9)^n, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\left(\frac{2}{9}\right)^{n}$$
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
$$a_{n} = 1$$
and
$$x_{0} = - \frac{2}{9}$$
,
$$d = 1$$
,
$$c = 0$$
then
False

Let's take the limit
we find
False
The rate of convergence of the power series
2/7
$$\frac{2}{7}$$
2/7
0.285714285714285714285714285714
0.285714285714285714285714285714`