Question

hãy chứng tỏ rằng

2 / 2 x 5 + 2/ 5 x 8 + 2 / 8 x 11 +  2 / 11 x 14 + 2 / 14 x 17  <  1

nhanh nhé^^

Answer 1

Ta có : \(\frac{2}{2.5}+\frac{2}{5.8}+\frac{2}{8.11}+\frac{2}{11.14}+\frac{2}{14.17}\)

\(=\frac{2}{3}\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}\right)\)

\(=\frac{2}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+.....+\frac{1}{14}-\frac{1}{17}\right)\)

\(=\frac{2}{3}\left(\frac{1}{2}-\frac{1}{17}\right)=\frac{2}{3}.\frac{15}{34}=\frac{5}{17}< 1\)

Answer 2

nó = 2/3(3/2x5+3/5x8+...+3/14x17)

=2/3(1/2-1/5+1/5-1/8+...+1/14-1/17)

=2/3x(1/2-1/17)

=2/3x15/34=5/17<1( điều phải chứng minh)