Our instructor assigned a problem from Rudin's Principles of Mathematical Analysis; a problem which I have been unable to solve after giving it good thought. The statement is: "Prove that the convergence of SUM[an] implies the convergence of SUM[sqrt(an)/n], if an >= 0." The instructor did give us a hint: "Review the ideas of chapter one," from which I gleaned the archimedean property or supremums might be important. Anyway, if anyone is familiar with how this can be proved, I would appreciate a nudge in the right direction. Thanks.