Chứng minh bất đẳng thức: A = 36/(1x3x5) + 36/(3x5x7) +...+ 36/(25x27x29) < 3

\(\frac{4}{1\times3\times5}=\frac{1}{1\times3}-\frac{1}{3\times5}\)

\(\frac{4}{3\times5\times7}=\frac{1}{3\times5}-\frac{1}{5\times7}\)

...

=> \(A=\frac{36}{1\times3\times5}+\frac{36}{3\times5\times7}+\frac{36}{5\times7\times9}+...+\frac{36}{25\times27\times29}\)

\(A=9\left(\frac{4}{1\times3\times5}+\frac{4}{3\times5\times7}+\frac{4}{5\times7\times9}+...+\frac{4}{25\times27\times29}\right)\)

\(A=9\left(\frac{1}{1\times3}-\frac{1}{3\times5}+\frac{1}{3\times5}-\frac{1}{5\times7}+\frac{1}{5\times7}-\frac{1}{7\times9}+...+\frac{1}{25\times27}-\frac{1}{27\times29}\right)\)

\(A=9\left(\frac{1}{3}-\frac{1}{27\times29}\right)\)

\(A=3-\frac{9}{27\times29}\ <3\ \left(đpcm\right)\)

\(A=\frac{36}{1\times3\times5}+\frac{36}{3\times5\times7}+\frac{36}{5\times7\times9}+...+\frac{36}{25\times27\times29}\)

\(A=9\left(\frac{4}{1\times3\times5}+\frac{4}{3\times5\times7}+\frac{4}{5\times7\times9}+...+\frac{4}{25\times27\times29}\right)\)

\(A=9\left(\frac{1}{1\times3}-\frac{1}{3\times5}+\frac{1}{3\times5}-\frac{1}{5\times7}+\frac{1}{5\times7}-\frac{1}{7\times9}+...+\frac{1}{25\times27}-\frac{1}{27\times29}\right)\)

\(A=9\left(\frac{1}{3}-\frac{1}{27\times29}\right)\)

\(A=3-\frac{9}{27\times29}\ <3\ \left(đpcm\right)\)

Cám ơn ạ