Hello sir/ madam
I am really confused about this topic, and i am unable to understand it well. So please help me! I need to send me, clear, detailed and main notes about the principle of mathematical Induction, proofs, and applications. And I would be pleased if you sent me, some solved problems for more
clarification and understanding.
I would like to appreciate your help! Thank You!
I think of mathematical induction like climbing a ladder. You want to prove that you could (theoretically) get to the top of the ladder, without actually climbing every step. There are two basic steps to the proof:
- Prove that you can get to the first rung of the ladder so you can start climbing.
[This is sometimes called proving the "base case", or "the case for n=1" (or 0, or 2, - this number depends on the question) ]
- Prove that if you are standing on some rung of the ladder, that you can climb to the next rung.
[This is the inductive step. This usually involves assuming the thing you want to prove is true for a natural number n, and then showing that this somehow implies the result is true for n+1.]
If you can prove these two steps, then the Principle of Mathematical Induction says that no matter how many rungs the ladder has, you can climb it.
[or, the statement you are trying to prove will be true for any natural number n (the natural numbers are the counting numbers, starting at either 0 or 1, depending on which school of thought you side with). ]
This previously answered question has an example: