How do I apply mathematical induction to answer questions

If you are familiar with induction but unsure how to answer the types of questions that require it, a structure can be useful.
Even when confident, it will help an examiner to see where to award you marks if you display your working as follows.
Base case: Stating or proving why the result youre asked to prove is true for n=1 or n=0.
Assumption: We needn't know that this is true, here we simply write that we assume there is some value of n=k, for which the result is true.
Induction Step: This is often the trickiest part. All the other steps are the same whatever question you may be tackling, however here you need to conclude the statement in question holds for n=k+1 if it hold for n=k. Usually this will involve a few steps of algebra.
Conclusion: All thats left to do now is state "By mathematical induction, [the result] is true for all n".

With this in mind you may need to practice some examples to get used to what could be required for an induction step. Here's one to try yourself or go through with a tutor:Show that 4^n - 1 is divisible by 3 for all intergers n. [Hint: X is divsible by three is equivalent to X is equal to three times some other integer]