Question

counterexample of 9^n -1 is divisble by 8

Answer 1

\(\normalsize\color{blue}{ 9^{~n-1} }\) by 8 ?

Answer 2

when I see the power of n-1 I think of derivatives.

Answer 3

What do you think ?

Answer 4

I am guessing its \(9^n-1\)

Answer 5

I would say either way it is ....

Answer 6

Not telling the answer straight out

Answer 7

yeah....

Answer 8

The first two steps will be provided. For step 3, match the right and left sides of the equation to prove the statement.
Step 1: When n = 1, 9n -1 = 91 - 1 = 8. Eight is divisible by 8, so the equation is true for n = 1
Step 2: Assume that 9k-1 is divisible by 8 for some positive integer, k. This means that there is a whole number r such that 9k-1 = 8r
Step 3: Show that the statement n = k + 1 is true
9^k -1
9^k
9(9^k)
9^k+1
9^k-1 -1

answers:
8r
8r+1
72r+9
9(8r+1)
8(9r+1)
72r+8