Hi guys, here I am again! I've been doing fine, even mowing through with what I feel are normal Inductive Proof Questions like:

1 x 3 x 5 + 2 x 4 x 6 + ... + n(n+2)(n+4) = (n/4)(n+1)(n+4)(n+5)

but now I've hit a point in the book where it doesn't feel so straightforward, and honestly I still don't get it.

Point 1. Just to clarify for myself, in proof by induction, the goal is to take the next step on the left hand side of the statement, and stick it onto the right hand side as well, then, using mathematical techniques learnt factorize the right hand side so every n becomes n+1 to indicate that the statement is still true for whatever value n is.

Point 2. The textbook has started asking questions that kind of boggle me, but I believe it's because I might be missing some small technique or approach to solving them. An example of these questions involve:

Question 1:

Use Proof by induction to prove that:

(x-1) is a factor of x^{n - 1}-1

for all positive integer values of n

Question 2:

Use Proof by induction to prove that:

1 x 2 x 3 x 4 x 5 x 6 x ... x n ≥ 3^{n}

where n > 6

Question 3:

Use Proof by induction to prove that:

7^{n} + 2 * 13^{n}

is a multiple of 3 for all n ≥ 0

These types of questions definitely don't follow the styles of the questions they come after. Its really the Inductive Step that I get trouble with.

Could it possibly because my point 1(somewhere above) is wrong?

Note: Please don't give me the answers because I don't have many of these questions. Maybe just a pointer or direction?

Thanks!