Principle of Mathematical Induction

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

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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.

These are the comment from my math professor about this paper ” do not see clearly the induction step.

You need to prove:

(a) The formula P(n) is true for n=1
(b) If the formula is true for an n then it follows that it will be true for the next one n+1
As a conclusion: the formula P(n) is true for all natural numbers.

Sample Solution

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