285 L26 Mathematical Induction; Binomial Theorem Mathematical InductionMathematical inductionis a method for proving mathematical statements which involve natural numbers. We denote a statement ( )A n, nis natural. Example: ( )A n: 246...(2 )(1)nn n++++=+, 1, 2, 3,n=…. The Principle of Mathematical Induction:Suppose that the following two conditions are satisfied with regard to a statement ( )A n: 1. ( )A nis true for 0nn=. 2. If ( )A nis true for nk=(0kn≥), it is also true for 1nk=+. Then ( )A nis true for all natural numbers 0nn≥. 286 Example: Use mathematical induction to prove that the formulas are valid. ( )A n: (1)123...2n nn+++++=, 1n≥
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