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200(0.98)^n-1
Sum of series/ 200(0.98)^n-1

Sum of series 200(0.98)^n-1


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The solution

You have entered [src] 
  oo                 
____                 
\   `                
 \    /        n    \
  \   |    /49\     |
  /   |200*|--|  - 1|
 /    \    \50/     /
/___,                
n = 1
$$\sum_{n=1}^{\infty} \left(200 \left(\frac{49}{50}\right)^{n} - 1\right)$$ 
Sum(200*(49/50)^n - 1, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$200 \left(\frac{49}{50}\right)^{n} - 1$$
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
$$a_{n} = 200 \left(\frac{49}{50}\right)^{n} - 1$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} \left|{\frac{200 \left(\frac{49}{50}\right)^{n} - 1}{200 \left(\frac{49}{50}\right)^{n + 1} - 1}}\right|$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
-oo
$$-\infty$$ 
-oo
Numerical answer
The series diverges
The graph
Sum of series 200(0.98)^n-1

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