Question

[Lê Thị Huyền Trang]

cho A= 1/4^2+ 1/5^2+ 1/6^2+....+1/10^2

chung minh A <7/44

Answer 1

[ღ๖ۣۜLinh's ๖ۣۜLinh'sღ] ★we are one★]

\(\frac{1}{4^2}+\frac{1}{5^2}+...+\frac{1}{10^2}< \frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{9.10}< \frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...\frac{1}{9}-\frac{1}{10}\)

=> \(A< \frac{1}{4}-\frac{1}{10}=\frac{3}{30}=\frac{21}{210}\)

Ta lại có \(\frac{7}{44}=\frac{21}{132}>\frac{21}{210}\)

=> \(A< \frac{7}{44}\)