Question

\(S=\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{9^2}\)

Chứng minh S<4/5

Answer 1

Câu hỏi của Raf - Toán lớp 6 - Học toán với OnlineMath

Answer 2

<br class="Apple-interchange-newline"><div id="inner-editor"></div>122 +132 +142 +...+192  <   11.2 +12.3 +13.4 +14.5 +...+18.9 

Answer 3

\(S=\frac{1}{2^2}+\frac{1}{3^2}+....+\frac{1}{9^2}\)

\(S=\frac{1}{2.2}+\frac{1}{3.3}+.......+\frac{1}{9.9}\)

\(S< \frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{9.10}\)

\(S< \frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{9}-\frac{1}{10}\)

\(S< \frac{1}{2}-\frac{1}{10}\)

\(S< \frac{2}{5}< \frac{4}{5}\)

\(\Rightarrow S< \frac{4}{5}\)