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Sum of series log(1-3/n2)

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  oo             
 ___             
 \  `            
  \      /    3 \
   )  log|1 - --|
  /      \    n2/
 /__,            
n = 1

\sum_{n=1}^{\infty} \log{\left(1 - \frac{3}{n_{2}} \right)}

Sum(log(1 - 3/n2), (n, 1, oo))

The radius of convergence of the power series

Given number:

\log{\left(1 - \frac{3}{n_{2}} \right)}

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} = \log{\left(1 - \frac{3}{n_{2}} \right)}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty} 1

True

False

The answer [src]

      /    3 \
oo*log|1 - --|
      \    n2/

\infty \log{\left(1 - \frac{3}{n_{2}} \right)}

oo*log(1 - 3/n2)