因为当k≥2时,1/√k=2/(2√k)＜2/(√k+√(k-1))=2(√k-√(k-1)).
所以
1+1/√2+1/√3+⋯+1/√n＜1+2(√2-√1)+2(√3-√2)+⋯+2(√n-√(n-1))=2√n-1