Question

[Lê Thị Huyền Trang]

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

chung minh A<7/44

Answer 1

[Huỳnh Quang Sang]

\(A=\frac{1}{4^2}+\frac{1}{5^2}+...+\frac{1}{10^2}>\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+...+\frac{1}{10\cdot11}\)

\(=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{10}-\frac{1}{11}\)

\(=\frac{1}{4}-\frac{1}{11}=\frac{7}{44}\)

Kết luận : ....

Answer 2

[An Nguyễn]

Ta có  : \(\frac{1}{4^2}< \frac{1}{3.4}\)

           \(\frac{1}{5^2}< \frac{1}{4.5}\)

\(................................\)

        \(\frac{1}{10^2}< \frac{1}{9.10}\)

\(\Rightarrow\frac{1}{4^2}+\frac{1}{5^2}+...+\frac{1}{10^2}< \frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\)

\(\Rightarrow A< \frac{1}{3}-\frac{1}{4} +\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\)

\(\Rightarrow A< \frac{1}{3}-\frac{1}{10}=\frac{7}{30}\)

Mà \(\frac{7}{30}< \frac{7}{44}\)=> \(A< \frac{7}{44}\)(đpcm)

Chúc bn hok tốt ^.^