用凸函数性质证明一类数列不等式

Using Convex Function Nature to Prove a Type of Sequence Inequality

利用连续凸函数在等分点上函数值的性质,证明了一类含有递增差数列的奇项和与偶项和相比的不等式,以及连续凸函数在闭区间的等分点上之函数值构成了一个增差数列。

Based on the nature of continuing convex function in equal diversion point, an inequality is proved which contains the odd item and the even item sumsa of increasing difference sequence, and the function value, which is obtained through the closed interval of the continuing convex function at the equal diversion point, forms a increasing difference sequence.