众所周知,著名的加权算术平均与加权几何平均不等式是:设ai,pi0,i=1,2,…,n,且sum from i=1 to n 1/pi=1,则sum from i=1 to n 1/(pi)ai≥multiply from i=1 to n 1/a_i~(pi),(1)其中等式当且仅当a1=a2=…=an时成立.本短文将给出此经典不等式的一个改进.定理1设0ai1,pi1,i= It is well-known that the well-known weighted arithmetic mean and weighted geometric mean inequalities are: from ai, pi0, i = 1,2, ..., n and sum from i = 1 to n1 / pi = (1) where the equation holds if and only if a1 = a2 = ... = an. This essay will give this classic An improvement of inequality Theorem 1 Let 0ai1, pi1, i =