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(3^k)/(5^k)

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  • Sum of series:
  • x^n/n
  • 1/(4n^2-1) 1/(4n^2-1)
  • (7^n-2^n)/14^n (7^n-2^n)/14^n
  • 3^(n-1)/8^(n-1) 3^(n-1)/8^(n-1)

  • Identical expressions

  • (three ^k)/(five ^k)
  • (3 to the power of k) divide by (5 to the power of k)
  • (three to the power of k) divide by (five to the power of k)
  • (3k)/(5k)
  • 3k/5k
  • 3^k/5^k
  • (3^k) divide by (5^k)
Sum of series/ (3^k)/(5^k)

Sum of series (3^k)/(5^k)


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The solution

You have entered [src] 
  oo    
____    
\   `   
 \     k
  \   3 
   )  --
  /    k
 /    5 
/___,   
k = 0
$$\sum_{k=0}^{\infty} \frac{3^{k}}{5^{k}}$$ 
Sum(3^k/5^k, (k, 0, oo))
The radius of convergence of the power series
Given number:
$$\frac{3^{k}}{5^{k}}$$
It is a series of species
$$a_{k} \left(c x - x_{0}\right)^{d k}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{k \to \infty} \left|{\frac{a_{k}}{a_{k + 1}}}\right|}{c}$$
In this case
$$a_{k} = 3^{k}$$
and
$$x_{0} = -5$$
,
$$d = -1$$
,
$$c = 0$$
then
$$\frac{1}{R} = \tilde{\infty} \left(-5 + \lim_{k \to \infty}\left(3^{k} 3^{- k - 1}\right)\right)$$
Let's take the limit
we find
False

False

$$R = 0$$
The rate of convergence of the power series
The answer [src] 
5/2
$$\frac{5}{2}$$ 
5/2
Numerical answer [src] 
2.50000000000000000000000000000
2.50000000000000000000000000000
The graph
Sum of series (3^k)/(5^k)

    Examples of finding the sum of a series

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