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2^(1.5*n)*0.5^(n-1)*0.5^(n)

  • How to use it?

  • Sum of series:
  • (2/3)^n (2/3)^n
  • (1+(-3)^n)/6^n (1+(-3)^n)/6^n
  • sin(1/(n*sqrt(n)))*x^n
  • 2^(1.5*n)*0.5^(n-1)*0.5^(n) 2^(1.5*n)*0.5^(n-1)*0.5^(n)

  • Identical expressions

  • two ^(one . five *n)* zero . five ^(n- one)* zero . five ^(n)
  • 2 to the power of (1.5 multiply by n) multiply by 0.5 to the power of (n minus 1) multiply by 0.5 to the power of (n)
  • two to the power of (one . five multiply by n) multiply by zero . five to the power of (n minus one) multiply by zero . five to the power of (n)
  • 2(1.5*n)*0.5(n-1)*0.5(n)
  • 21.5*n*0.5n-1*0.5n
  • 2^(1.5n)0.5^(n-1)0.5^(n)
  • 2(1.5n)0.5(n-1)0.5(n)
  • 21.5n0.5n-10.5n
  • 2^1.5n0.5^n-10.5^n

  • Similar expressions

  • 2^(1.5*n)*0.5^(n+1)*0.5^(n)
Sum of series/ 2^(1.5*n)*0.5^(n-1)*0.5^(n)

Sum of series 2^(1.5*n)*0.5^(n-1)*0.5^(n)


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The solution

You have entered [src] 
  oo                 
____                 
\   `                
 \     3*n           
  \    ---           
  /     2   1 - n  -n
 /    2   *2     *2  
/___,                
n = 1
$$\sum_{n=1}^{\infty} \left(\frac{1}{2}\right)^{n} \left(\frac{1}{2}\right)^{n - 1} \cdot 2^{\frac{3 n}{2}}$$ 
Sum((2^(3*n/2)*(1/2)^(n - 1))*(1/2)^n, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\left(\frac{1}{2}\right)^{n} \left(\frac{1}{2}\right)^{n - 1} \cdot 2^{\frac{3 n}{2}}$$
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
$$a_{n} = 2^{1 - n}$$
and
$$x_{0} = -2$$
,
$$d = \frac{1}{2}$$
,
$$c = 0$$
then
$$\sqrt{R} = \tilde{\infty} \left(-2 + \lim_{n \to \infty}\left(2^{n} 2^{1 - n}\right)\right)$$
Let's take the limit
we find
False

False
The rate of convergence of the power series
The answer [src] 
    ___  
  \/ 2   
---------
      ___
    \/ 2 
1 - -----
      2
$$\frac{\sqrt{2}}{1 - \frac{\sqrt{2}}{2}}$$ 
sqrt(2)/(1 - sqrt(2)/2)
Numerical answer [src] 
4.82842712474619009760337744842
4.82842712474619009760337744842
The graph
Sum of series 2^(1.5*n)*0.5^(n-1)*0.5^(n)

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