本文拟出初等代数中一个新的不等式链,并获得一连等式。设a_1,a_2,…,a_n均是正实数,n≥2,且sum from i=1 to n a_i=n。记f(k)=1+a_k+a_ka_(k+1)+…+a_ka_(k+1)·…·a_na_1·…·a_(k-2);f_i(k)表示和f(k)(自左至右)的第i个和项,i=1,2,…,n。令S_i=sum from i=1 to n (f_i(k)/f(k)),i=1,2,…,n, 则有不等式链 This paper proposes a new chain of inequality in elementary algebra and obtains a series of equations. Let a_1, a_2, ..., a_n be positive real numbers, n≥2, and sum from i=1 to n a_i=n. Note that f(k)=1+a_k+a_ka_(k+1)+...+a_ka_(k+1)····a_na_1····a_(k-2); f_i(k) and f(k) ( (i) from left to right, the i-th term, i=1, 2, ..., n. Let S_i=sum from i=1 to n (f_i(k)/f(k)),i=1,2,...,n, then we have an inequality chain