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30000*(1,03)^n

  • How to use it?

  • Sum of series:
  • 3n 3n
  • nx^n!
  • (3-k)/(k*(k+3)*(k+1)) (3-k)/(k*(k+3)*(k+1))
  • sqrt(n)sin(1/(2n))^2 sqrt(n)sin(1/(2n))^2

  • Identical expressions

  • thirty thousand *(one , three)^n
  • 30000 multiply by (1,03) to the power of n
  • thirty thousand multiply by (one , three) to the power of n
  • 30000*(1,03)n
  • 30000*1,03n
  • 30000(1,03)^n
  • 30000(1,03)n
  • 300001,03n
  • 300001,03^n
Sum of series/ 30000*(1,03)^n

Sum of series 30000*(1,03)^n


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The solution

You have entered [src] 
  oo               
____               
\   `              
 \                n
  \          /103\ 
  /    30000*|---| 
 /           \100/ 
/___,              
n = 38
$$\sum_{n=38}^{\infty} 30000 \left(\frac{103}{100}\right)^{n}$$ 
Sum(30000*(103/100)^n, (n, 38, oo))
The radius of convergence of the power series
Given number:
$$30000 \left(\frac{103}{100}\right)^{n}$$
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
$$a_{n} = 30000$$
and
$$x_{0} = - \frac{103}{100}$$
,
$$d = 1$$
,
$$c = 0$$
then
False

Let's take the limit
we find
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 30000*(1,03)^n

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