Anonymous

# I need help with this question. Any help is appreciate! Use mathematical induction to prove that 4n - 1 is divisible by 3 for all n >= 1?

### 2 Answers

Relevance

- 6 months agoFavorite Answer
Did you mean 4^(n) - 1?

4^(1) - 1 = 4 - 1 = 3

4^(2) - 1 = 16 - 1 = 15

4^(3) - 1 = 64 - 1 = 63

4^(n) - 1 = 3k

4^(n) = 3k + 1

4^(n + 1) = 4 * (3k + 1)

4^(n + 1) = 12k + 4

4^(n + 1) = 12k + 3 + 1

4^(n + 1) - 1 = 12k + 3

4^(n + 1) - 1 = 3 * (4k + 1)

Well that looks familiar. Compare it to 4^(n) - 1 = 3k and assign no real values to n or k and we have the same basic form. And since 4^(n) - 1 is divisible by 3 and 4^(n + 1) - 1 is also divisible by 3, then that means that 4^(n + 2) - 1 will also be divisible by 3 and so on.

Still have questions? Get your answers by asking now.

The format didn't carry over to yahoo answers when i copy pasted, but this is the answer i was looking for. Thank you so much!