The topic will be: Principle of Mathematical Induction. In page 25 of the following book,
http://math.uga.edu/~pete/2400full.pdf
you have an introduction. In that same book link, in page 27, you can read about the first things that you can prove using induction. Basically it is used to prove a statement for all numbers n=1,2,… and what you do is to prove it for n=1 and to prove that if it is true the formula for some n it will also be true for the next one n+1. In this way it is true for all n.
Once you are a little familiar with this we can prove some calculus sums. See for example, the presentation http://people.ku.edu/~d982b169/math125section51.pdf
If it has enough Math, like the prove of the Riemann sums for a few functions, the number of pages will not be that important. Do not worry about the number of pages.
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