,设X=1+1/√2+1/√3+1/√4+………+1/√99+1/√100,求证18

Question

,设X=1+1/√2+1/√3+1/√4+………+1/√99+1/√100,求证18

Answer 1

1/√n=2/2√n1+2(√3-√2)+2(√4-√3)+……+2(√101-√100)
=1+2(√101-√2)>18