Ta có: 9/2.5 + 9/5.8 + 9/9.11+...+ 9/29.32
=>9.(1/2 -1/5 + 1/5 - 1/8 +...+1/29 -1/32)
=>9.( 1/2 -1/32)
=>9. 15/32
=>45/32
Suy ra 45/32 >1 nên S>1
Ta có: \(S=\dfrac{9}{2\cdot5}+\dfrac{9}{5\cdot8}+\dfrac{9}{8\cdot11}+...+\dfrac{9}{29\cdot32}\)
\(=3\left(\dfrac{3}{2\cdot5}+\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+...+\dfrac{3}{29\cdot32}\right)\)
\(=3\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{29}-\dfrac{1}{32}\right)\)
\(=3\left(\dfrac{1}{2}-\dfrac{1}{32}\right)\)
\(=3\cdot\dfrac{15}{32}=\dfrac{45}{32}>1\)
