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数学归纳法是一种重要的数学思想方法,主要用来证明猜想或证明与正整数有关的代数恒等式、三角恒等式、不等式、整除性、通项公式及几何性质。而不完全归纳法是从特殊出发,通过试验、观察、分析、综合、抽象慨括出一般性结论的一种重要方法。数学归纳法的表述严格、规范,三个步骤缺一不可,第一步是递推的“基础”;第二步是递推的“依据”;第二步中,归纳假设起着“一凑假设,二凑结论”的关键作用;第三步通过一定技巧推出n=k+1结论。
Mathematical induction is an important method of mathematics and is mainly used to prove the conjecture or proof of algebraic identities, trigonometric identities, inequalities, divisibility, general formulas and geometric properties related to positive integers. However, the incomplete induction method is an important method to set out the general conclusion through experiments, observation, analysis, synthesis and abstraction. Mathematical induction of the strict, normative, the three steps are indispensable, the first step is recursive “basis”; the second step is recursive “basis”; the second step, the induction hypothesis The key role of “a hash assumptions, second to make conclusions ”; the third step through certain skills introduced n = k +1 conclusions.