Question

设s=1+1/根号2+1/根号3+...+1/根号100,求S的整数部分

Answer 1

2)x=1+1/根号2+1/根号3+...+1/根号100

=1+2/2√2+2/2√3+…+2/2√100

>1+2/(√2+√3)+2/(√3+√4)+…+2/(√100+√101)

=1+2(√3-√2)+2(√4-√3)+…+2(√101-√100)

=1+2(√101-√2)