Ta có:
√1>√100=>1/√1>1/√100
√2>√100=>1/√2>1/√100
√3>√100=>1/√3>1/√100
......
√100=√100=>1/√100=1/√100
=>1/√1+1/√2+1/√3+...+1/√100>1/√100+1/√100+1/√100+...+1/√100(100 số hạng1/√100)
=>1/√1+1/√2+1/√3+...+1/√100>1/10+1/10+1/10+...+1/10(100 số hạng 1/10)
=>1/√1+1/√2+1/√3+...+1/√100>1/10x100
=>1/√1+1/√2+1/√3+...+1/√100>10
Vậy 1/√1+1/√2+1/√3+...+1/√100>10