Prove that 9 divides 4" + 6n – 1 for n > 1 by mathematical induction.

This is a classic problem I think that you mean

This problem clearly states to use proof by induction, follow the complete answer below.

Step-by-step explanation:

To prove something by induction we have to make a proposition first, in this case:

is divisible by 9

Where is the order of the proposition.

First we have to prove the first few orders, let's just check P(1):

which is clearly divisible by 9

Now let's assume that P(n) is true that means, our original proposition is true. Now let's try to find out whether P(n+1) is true:

The is divisible by 9 because we assumed that " is divisible by 9" was a true proposition. On the other hand has a factor of 9 regardless of n, thus is also divisible by 9 that means that P(n+1) is true and it follows that P(n) must also be true, thus proving our initial statement.