# How should I approach a proof by induction question?

Proof by induction is a powerful proof technique that can be used to prove a certain property and is a common question on the IB exams. Consider for instance the problem "Prove that sinx + sin3x +...+ sin((2n-1)x) = sin^2 n x/sinx". The essential components of an inductive proof are as follows:Consider the case when n = 1Assume true for n = k, for some kProve true by demonstrating that the pattern holds for n = k+1Conclude the proof.Step 2 just requires you to replace any instance of "n" in the problem with a "k". Proof by induction problems are often worth 6-7 marks on the exam, and doing steps 1 and 2 correctly is a surefire way of picking up 2-3 marks for free. A useful tip to consider after doing step 2 is that you should write the "goal"you are trying to achieve on the side. In other words, write out the k+1 case so you know what you're looking for as you work through the steps. The lovely thing about proof by induction is that you can easily do it by working through it formulaically. All you need is for your algebra skills to be solid!

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