P k P k 1 P k P k 1 If you can do that you have used mathematical induction to prove that the property P P is true for any element and therefore every element in the infinite set. Summary Principle of Mathematical Induction Formulas. 2k 1 k 2.
The statement is true for n k.
2k 2 k 1 k 1 k 2 and the proof by mathematical induction is complete. 3 k 1 1 3 3 k 1 2 3 k 3 k 1 The first part 2 3 k is certain to be a multiple of 2 and the second part 3 k 1 is also true as our previous assumption. The solution in mathematical induction consists of the following steps. Example if we are to prove that 1234nn n12 we say let P n be 1234nn n12.