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Sum of series 1/(n(log(n))^k)



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The solution

You have entered [src]
  oo           
____           
\   `          
 \        1    
  \   ---------
  /        k   
 /    n*log (n)
/___,          
n = 1          
$$\sum_{n=1}^{\infty} \frac{1}{n \log{\left(n \right)}^{k}}$$
Sum(1/(n*log(n)^k), (n, 1, oo))
The answer [src]
  oo          
____          
\   `         
 \       -k   
  \   log  (n)
  /   --------
 /       n    
/___,         
n = 1         
$$\sum_{n=1}^{\infty} \frac{\log{\left(n \right)}^{- k}}{n}$$
Sum(log(n)^(-k)/n, (n, 1, oo))

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