新教材中数学归纳法常见的几种题型

• 作 者: 吴军
• 机 构: 贵州省修文中学,
• 出 处: 新课程学习(上)
• 发表日期: 2014年06期

在高中数学选修2-2中,学习了数学证明中的数学归纳法,现在就数学归纳法常见的几种题型来和大家进行探讨,现在来看下面的几种题型。题型一:用数学归纳法证明等式例1.用数学归纳法证明:1×4+2×7+3×10+…+n(3n+1)=n(n+1)2(其中n∈N*).【证明】(1)当n=1时,左边=1×4=4,右边=1×22=4,左边=右边,等式成立.(2)假设当n=k(k∈N*)时等式成立,即1×4+2×7+3×10+…+k(3k+1)=k(k+1)2.

In high school mathematics elective 2-2, learning math induction mathematical deduction, and now several common types of mathematical induction to discuss with you, now look at the following types of questions. Problem 1: Prove the equation by mathematical induction Example 1. Prove by mathematical induction: 1 × 4 + 2 × 7 + 3 × 10 + ... + n (3n + 1) = n (n + 1) 2 (1) When n = 1, the left = 1 × 4 = 4, the right = 1 × 22 = 4, the left = the right, the equation holds. (2) Suppose that when n = k (k ∈ N *) holds, that is, 1 × 4 + 2 × 7 + 3 × 10 + ... + k (3k + 1) = k (k + 1) 2.