\(=4\left(\frac{4}{20.24}+\frac{4}{24.28}+...+\frac{4}{76.80}\right)\)
\(=4\left(\frac{1}{20}-\frac{1}{24}+\frac{1}{24}-\frac{1}{28}+...+\frac{1}{76}-\frac{1}{80}\right)\)
\(=4\left(\frac{1}{20}-\frac{1}{80}\right)\)
\(=4\times\frac{3}{80}\)
\(=\frac{12}{80}=\frac{3}{20}<1\)
đpcm
A=\(\frac{16}{20.24}+\frac{16}{24.28}+\frac{16}{28.32}+....+\frac{16}{76.80}\)
a) CMR: \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{n^2}< \frac{3}{4}\)
b) CMR: \(\frac{1}{3^2}+\frac{1}{5^2}+\frac{1}{7^2}+...+\frac{1}{\left(2n+1\right)^2}< \frac{1}{4}\)
CMR \(A=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{50^2}< \frac{4}{9},A>\frac{1}{4}\)
CMR:\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{99^2}+\frac{1}{100^2}< \frac{3}{4}\)\(\frac{3}{4}\)
CMR:\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{1990^2}< \frac{3}{4}\)
CMR
\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< \frac{3}{4}\)
cho S=\(\frac{1}{4}+\frac{2}{4^2}+\frac{3}{4^3}+...+\frac{2018}{4^{2018}}\)CMR: S<\(\frac{1}{2}\)
\(CMR:\frac{1}{4^2}+\frac{1}{6^2}+\frac{1}{8^2}+...+\frac{1}{\left(2n\right)^2}< \frac{1}{4}\)
CMR
B=\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2019^2}< \frac{3}{4}\)
