Prove by mathematical induction that

vittorecostao1

vittorecostao1

Answered question

2022-06-20

Prove by mathematical induction that a n is an irrational number.

Answer & Explanation

scipionhi

scipionhi

Beginner2022-06-21Added 25 answers

Basis: a 1 = a is irrational.

Induction: Suppose that a m , m odd, is irrational. Then a m + 2 = a m a 2 is an irrational number times a rational number, and therefore irrational.
Petrovcic2x

Petrovcic2x

Beginner2022-06-22Added 11 answers

If n is odd, then n + 2 is odd and so a n + 2 = a n a 2 is irrational, being the product of an irrational and a rational.

If you want to do induction in steps of 1 instead of 2, write n = 2 k + 1 and use induction on k.

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