论文部分内容阅读
中学数学教材中,给出的等差、等比数列的通项公式和前n项和的公式,实际上都是等差、等比数列的充要条件。这四个充要条件,我们还可进一步简化如下(下面定理中,a_n表示数列通项,S_n表示前n项和,A、B、p、r、k均表示常数): 定理二数列{a_n}为等差数列的充要条件是a_n=A_n+B。定理二数列{a_n}为等差数列的充要条件是S_n=An~2+B_n。
In mathematics textbooks for middle schools, the equations for the general equations and the general formulae for the first n terms of arithmetic and arithmetic progressions given in the mathematics textbooks for middle schools are actually the necessary and sufficient conditions for arithmetic and arithmetic progressions. These four necessary and sufficient conditions, we can further simplify as follows (in the following theorems, a_n represents a series of general terms, S_n represents the first n terms, and A, B, p, r, and k represent constants): Theorem two series {a_n } The necessary and sufficient condition for the arithmetic progression is a_n=A_n+B. The necessary and sufficient condition for theorem two series {a_n} to be an arithmetic progression is S_n=An~2+B_n.