一个涉及等差数列平方根不等式的加强

A Strengthening of an Inequality of Square Root of Arithmetic Procession

应用构造求和相消与待定系数法,建立关于等差数列{a_(k)}各项平方根倒数之和Σ_(k=m)^(n)1/√a_(k)的上、下限估计,加强了涉及等差数列的若干已有结论.

The estimated bounds of Σ_(k=m)^(n)1/√a_(k),the sum of reciprocals of the square root of each part of arithmetic procession{a_(k)}ka,are established by applying the structured summation approach and the method of undetermined coefficients.Thus,the conclusions of series of equal differences involved are strengthened.