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 $\left( 1 + \dfrac{1}{n} \right)^n$ greater than 2.5?

정답·풀이 보기 (영어 원문)

For each natural number $n$ , if $n \geq 6$ , then $\left( 1 + \dfrac{1}{n} \right)^n > 2.5$ .

한 번 더 — 비슷한 문제Sundstrom, 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 $1 + 2^n$ ?

다 풀었으면 정답 확인

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