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Sum of series/ n^(1/n)

Sum of series n^(1/n)

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  oo       
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  \   n ___
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n = 1

\sum_{n=1}^{\infty} n^{\frac{1}{n}}

Sum(n^(1/n), (n, 1, oo))

The radius of convergence of the power series

Given number:

n^{\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} = n^{\frac{1}{n}}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty}\left(n^{\frac{1}{n}} \left(n + 1\right)^{- \frac{1}{n + 1}}\right)

True

False

The rate of convergence of the power series

The graph