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## Main Question or Discussion Point

**help needed urgently: Basic Math Induction**

I am trying to teach myself mathematical induction, have never encountered this before and it's giving me trouble. My problem will likely be very easy to you all so please forgive me.

I have put up the scanned image of the example in my book.

http://img89.imageshack.us/my.php?image=induct3zv.jpg

here are my 3 questions:

**(1)**What I don't understand is that how do I get the values in #2 (red ink) from #1. It seems like it's some basic factoring operation but I'm very confused even looking at this example. I have tried to get the values in #2 from #1 but they don't match up. It seems like the text decided to jump a step or maybe I just don't understand it's simple steps.

**(2)**How do we know when we've completely solved an inducation problem? for eg: in addition we know we've arrived at the answer when we can't add anymore. :D How do we know when we've solved the problem in induction?

**(3)**I would appreciate it if you can give me some basic tips regarding and how to do induction problems. This book I have doesn't go into it much besides showing examples. I think I understand most of it after having looked at three examples and stressing myself out the past 2 days trying to learn. The book just gives me the basic principles for inducation (1)Prove that it is true for n=1 (2)Assume it is true for n=k (3) use this to prove that n=k+1 is true. I would also be greatful if you can recommend me any good books regarding basic Algegra & Geometry.

Please help me as I'm taking this self learning course and don't have anyone to ask for help. I have an entrance exam in less than three weeks. Appreciate all kind help :D