if someone could help with this induction question that would be much appreciated
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Hey again! Okay, I can help with this one. So the prove by induction, we use three steps:
Step 1: We prove for the lowest integer value we need to satisfy the condition (in this case, 1). So we just sub that in and check if it is divisible by three, which it is.
Step 2: We assume that the condition is true for
, where k is some integer which meets our conditions. This just sets up a general case, which
hasn't been proven yet. We let this condition be:
Such that
is some integer. This is how we denote divisibility in all induction questions.
We now test for
. Now there are several ways to proceed, but I think the easiest to understand is immediately bring the previous line into the expression, we use the assumption in our proof. Hopefully this makes sense:
Which is divisible by 3, since M is an integer.
Step 3: Since the expression
is divisible by three, then the result is true for
. However, since the result is true for n=1, this means that by induction, it is true for n=1+1=2, n=2+1=3, etc, for all
Hope that this helped!