Writing proofs by induction with divisibility is a bit trickier than with sequences, series, and matrices because:

1. you don’t have a formula directly connecting the (k+1)’th thing to the k’th

2. what you do in Step 2 is definitely a chain of *reasoning* – a series of *statements* each one of which follows logically from the ones before – and not a chain of *working* – a series of expressions each of which is calculated to be equal to the one before. And you’re more used to chains of *working*, though in fact chains of *reasoning* are much more important in real-life maths.

Anyway, if it’s not clear in your mind, this may help: three methods compared for the example worked through in the textbook on page 127.

Click here to get the pdf.

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