



 
We have two responses for you The statement of your questions may have a misleading misprint in it, however, you are assuming that for some k ≥ 1 that you know p(k) is true. In essence that you have checked out p(n) for n = 1 all the way up to n = k, and now you want to use that information (that p(k) is true) to deduce the truth of the statement for n = k+1. The most common error I see from students is a statement like " we've checked p(1) is true, now assume p(n) is true for n ≥ 1"; that says assume that it's true for all n, which is what you're trying to prove. Penny
Iris, The Principle of Mathematical Induction is a theorem. It goes like this. Suppose you have a statement that involves the integer n. Let's call it p(n).
then you can conclude that the statement is true for every integer n greater than or equal to 1. Normally a proof by induction has four main parts:
For a longer explanation and some examples, try looking at Victoria  


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