1++>1,
1++++++>,
1+++...+>2,
...,
请你归纳出一般性结论:______________.
(2)已知f(x)=,设f1(x)=f(x),fn(x)=fn-1(fn-1(x))(n>1,且n∈N*),则f3(x)的表达式为________,猜想fn(x)(n∈N*)的表达式为________.
[解析] (1)观察不等式左边,各项分母从1开始依次增大1,且终止项为2n-1,不等式右边依次为,,,,...,从而归纳得出一般结论:1+++...+>.
(2)∵f(x)=,∴f1(x)=.
又∵fn(x)=fn-1(fn-1(x)),
∴f2(x)=f1(f1(x))==,
f3(x)=f2(f2(x))==,
f4(x)=f3(f3(x))==,
f5(x)=f4(f4(x))==,
∴根据前几项可以猜想fn(x)=.
[答案] (1)1+++...+>