Thread: 2 Induction Problems

1. Prove, by induction, that for every positive integer n,

Base case, n=1,

Assume:

Then I could write is as

I have no idea how to proceed.

If we assume that means

So times it by 4 for and there you go.

Originally Posted by Matt Westwood

If we assume that means

So times it by 4 for and there you go.

so all we cares about is the 4^n, it is always divisible by 6, the constant doesn't matter?

No, 4^n always leaves a remainder 4 when divided by 6. As 14 leaves a remainder 2 when divided by 6, so add them together and the sum is then divisible by 6.