\(\frac{3}{1.4}+\frac{3}{2.6}+\frac{3}{3.8}+...+\frac{1}{2012.1342}\)

\(=\frac{3}{1.4}+\frac{3}{2.6}+\frac{3}{3.8}+...+\frac{3}{2012.4026}\)

\(=\frac{6}{2.4}+\frac{6}{4.6}+\frac{6}{4.8}+...+\frac{6}{4024.4026}\)

\(=3\cdot\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{4024.4026}\right)\)

\(=3\cdot\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{4024}-\frac{1}{4026}\right)\)

\(=3\cdot\left(\frac{1}{2}-\frac{1}{4026}\right)\)

\(=3\cdot\frac{1}{2}-3\cdot\frac{1}{4026}\)

\(=1,5-\frac{3}{4026}< 1,5\)

\(A=\dfrac{3}{1.4}+\dfrac{3}{2.6}+\dfrac{3}{3.8}+...............+\dfrac{1}{2012.1342}\)

\(A=\dfrac{3}{1.4}+\dfrac{3}{2.6}+\dfrac{3}{3.8}+...........................+\dfrac{3}{2012.4026}\)

\(A=\dfrac{6}{2.4}+\dfrac{6}{4.6}+\dfrac{6}{6.8}+..........................+\dfrac{6}{4024.4026}\)

\(A=3\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+...................+\dfrac{2}{4024.4026}\right)\)

\(A=3\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+....................+\dfrac{1}{4024}-\dfrac{1}{4026}\right)\)

\(A=3\left(\dfrac{1}{2}-\dfrac{1}{4026}\right)\)

\(A=3.\dfrac{1}{2}-3.\dfrac{1}{4026}\)

\(A=1,5-\dfrac{3}{4026}< 1,5\)

Ta có

A = \(\dfrac{3}{1.4}\) + \(\dfrac{3}{2.6}\) + \(\dfrac{3}{3.8}\) + ... + \(\dfrac{1}{2012.1342}\)

A = \(\dfrac{3}{1.4}\) + \(\dfrac{3}{2.6}\) + \(\dfrac{3}{3.8}\) + ... + \(\dfrac{3}{2012.4026}\)

A = \(\dfrac{6}{2.4}\) + \(\dfrac{6}{4.6}\) + \(\dfrac{6}{6.8}\) + ... + \(\dfrac{6}{4024.4026}\)

A = \(3\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+...+\dfrac{2}{4024.4026}\right)\)

A = \(3\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{4024}-\dfrac{1}{4026}\right)\)

A = \(3\left(\dfrac{1}{2}-\dfrac{1}{4026}\right)\)

A = 3.\(\dfrac{1}{2}\) - 3.\(\dfrac{1}{4026}\)

A = 1,5 - \(3.\dfrac{1}{4026}\) < 1,5

=> A < 1,5

=> đpcm

Cô @Bùi Thị Vân hình như có gì đó nhầm lẫn!!

\(A=\)\(\frac{3}{1.4}\)\(+\)\(\frac{3}{2.6}\)\(+\)\(\frac{3}{2.8}\)\(+\).........\(+\)\(\frac{1}{2012.1342}\)\(< 1,5\)

\(=\)\(\frac{3}{1.4}\)\(+\)\(\frac{3}{2.6}\)\(+\)\(\frac{3}{3.8}\)\(+\)............\(+\)\(\frac{3}{2012.4026}\)

\(=\)\(\frac{6}{2.4}\)\(+\)\(\frac{6}{4.6}\)\(+\)\(\frac{6}{6.8}\)\(+\)..............\(+\)\(\frac{6}{4024.4026}\)

\(=\)\(3.\)\(\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...........+\frac{2}{4024.4026}\right)\)

\(=\)\(3.\)\(\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+....+\frac{1}{4024}-\frac{1}{4026}\right)\)

\(=\)\(3.\)\(\left(\frac{1}{2}-\frac{1}{4026}\right)\)

\(=\)\(3.\)\(\frac{1}{2}\)\(-\)\(3.\)\(\frac{1}{4026}\)

\(=\)\(1,5\)\(-\)\(\frac{3}{4026}\)\(< \)\(1,5\)

Vậy \(A< 1,5\)

B=1/1x4+1/4x3+1/3x8+...+1/7x16+1/16x9+1/9x20

2B=2x(1/4+1/12+1/24+...+1/112+1/144+1/180

2B=2/8+2/24+2/48+...+2/224+2/288+2/360

2B=2/2x4+2/4x6+2/6x8+...+2/14x16+2/16x18+2/18x20

2B=1/2-1/4+1/4-1/6+1/6-1/8+...+1/14-1/16+1/16-1/18+1/18-1/20

2B=1/2-1/20

2B=9/20

B=9/20:2

B=9/40