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  Volume 4, Issue 1, Article 2
 
Note on the Carleman's Inequality for a Negative Power Number
    Authors: Vu Duy Linh Nguyen, Thi Thu Van Nguyen, Thanh Long Nguyen,  
    Keywords: Carleman's inequality.  
    Date Received: 30/10/02  
    Date Published: 25/11/02  
    Subject Codes:

26D15

  
    Editors: Hüseyin Bor,  
 
    Abstract:

By the method of indeterminate coefficients we prove the inequality

$displaystyle sum_{n=1}^{infty }frac{n}{frac{1}{a_{1}}+frac{1}{a {2}}+...+frac{1}{%% a_{n}}}$

$displaystyle leq 2sum_{n=1}^{infty }left( 1-frac{1}{3n+1}%% -4n^{2}sum_{k=n}^{infty }frac{1}{k(k+1)^{2}(3k+1)(3k+4)}right) a_{n}, $

where