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(1-0.9)^(1/n)

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  • Sum of series:
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  • Identical expressions

  • (one - zero . nine)^(one /n)
  • (1 minus 0.9) to the power of (1 divide by n)
  • (one minus zero . nine) to the power of (one divide by n)
  • (1-0.9)(1/n)
  • 1-0.91/n
  • 1-0.9^1/n
  • (1-0.9)^(1 divide by n)

  • Similar expressions

  • (1+0.9)^(1/n)
Sum of series/ (1-0.9)^(1/n)

Sum of series (1-0.9)^(1/n)


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The solution

You have entered [src] 
  oo              
 ___              
 \  `             
  \   n __________
  /   \/ 1 - 9/10 
 /__,             
n = 1
$$\sum_{n=1}^{\infty} \left(- \frac{9}{10} + 1\right)^{\frac{1}{n}}$$ 
Sum((1 - 9/10)^(1/n), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\left(- \frac{9}{10} + 1\right)^{\frac{1}{n}}$$
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
$$a_{n} = \left(\frac{1}{10}\right)^{\frac{1}{n}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(10^{- \frac{1}{n}} 10^{\frac{1}{n + 1}}\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
  oo       
____       
\   `      
 \      -1 
  \     ---
  /      n 
 /    10   
/___,      
n = 1
$$\sum_{n=1}^{\infty} \left(\frac{1}{10}\right)^{\frac{1}{n}}$$ 
Sum((1/10)^(1/n), (n, 1, oo))
Numerical answer
The series diverges
The graph
Sum of series (1-0.9)^(1/n)

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