Question

 

chứng tỏ rằng \(\frac{3}{5x11}\)+ \(\frac{5}{11x21}\) + \(\frac{7}{21x35}\)+\(\frac{9}{35x53}\)   <  1                          

Answer 1

Đặt \(A=\frac{3}{5.11}+\frac{5}{11.21}+\frac{7}{21.35}+\frac{9}{35.53}\)

\(2A=\frac{6}{5.11}+\frac{10}{11.21}+\frac{14}{21.35}+\frac{18}{35.53}\)

\(2A=\frac{1}{5}-\frac{1}{11}+\frac{1}{11}-\frac{1}{21}+\frac{1}{21}-\frac{1}{35}+\frac{1}{35}-\frac{1}{53}\)

\(2A=\frac{1}{5}-\frac{1}{53}\)

\(2A=\frac{48}{265}\)

\(A=\frac{48}{265}:2\)

\(A=\frac{24}{265}\)

Vì \(\frac{24}{265}< 1\)nên \(A< 1\)(Điều phải chứng tỏ)

Ủng hộ mk nha !!! ^_^