Question

Prove that for any positive integer n, 7 evenly divides 9n - 2n.

Answer 1

To prove that 7 evenly divides 9n - 2n for any positive integer n, we can simplify the expression and show that it is a multiple of 7.

Step-by-step explanation:

To prove that for any positive integer n, 7 evenly divides 9n - 2n, we need to show that the difference 9n - 2n is divisible by 7.

Step 1: Simplify the expression 9n - 2n by combining like terms. This gives us 7n.

Step 2: Since 7n is a multiple of 7 for any positive integer n, we can conclude that 7 evenly divides 9n - 2n.