Question

 Chứng mjnh rằng: 

    3/1².2² +5/2².3² +7/3².4²+....+19/ 9².10²<1

Answer 1

\(\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+...+\frac{19}{9^2.10^2}=\frac{3}{1.4}+\frac{5}{4.9}+...+\frac{19}{81.100}\)

\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{9}+...+\frac{1}{81}-\frac{1}{100}=1-\frac{1}{100}