수학적 귀납법 연습문제 — Sundstrom, Mathematical Reasoning · 4.2절

Sundstrom, Mathematical Reasoning · 4.2절영어 원문

Formulate a conjecture (with an appropriate quantifier) that can be used as an answer to each of the following questions.

For which natural numbers $n$ is $3^n$ greater than $1 + 2^n$ ?

정답·풀이 보기 (영어 원문)

For each natural number $n$ , if $n \geq 2$ , then $3^n > 1 + 2^n$ .

한 번 더 — 비슷한 문제Sundstrom, Mathematical Reasoning · 4.1절 · 14번영어 원문

Use mathematical induction to prove that the sum of the cubes of any three consecutive natural numbers is a multiple of 9.

다 풀었으면 정답 확인

Three consecutive natural numbers may be represent by $n$ , $n + 1$ , and $n + 2$ , where $n$ is a natural number. For the inductive step, think before you try to do a lot of algebra. You should be able to complete a proof of the inductive step by expanding the cube of only one expression.

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