Question

chung minh rang :

1/2 + 1/3 +1/4 + 1/5 + 1/6 + 1/7 + 1/8 +1/9 > 8/9

jup minh nha a hi hi

Answer 1

Ta có:

8/9=1/9+1/9+1/9+1/9+1/9+1/9+1/9+1/9

Mà 1/9<1/2;1/9<1/3;...1/9<1/8;1/9=1/9

=>1/9+1/9+...+1/9<1/2+1/3+...+1/8+1/9

Vậy.......

Answer 2

\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\)>\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\)

\(=\frac{1}{1}-\frac{1}{9}\)

\(=\frac{8}{9}\)

Nên > \(\frac{8}{9}\)

Answer 3

\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{9}>\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{8.9}\)

\(\Rightarrow\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{9}>1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}\)

\(\Rightarrow\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{9}>1-\frac{1}{9}\)

\(\Rightarrow\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{9}>\frac{8}{9}\)

\(\RightarrowĐPCM\)