In my book there is a following example:

Prove by induction that 3 is a factor of$\displaystyle 4^n-1 $

the example has one step which baffles(in addition to the fact that I´m already baffled by induction as it is)

$\displaystyle

4^{k+1} -1=4(4^k)-1$

$\displaystyle = 4(4^k-1+1)-1 $ (why do you first subtract 1 and then add 1? Is this the mathematician´s creativity?)

$\displaystyle =4(4^k-1)+4(1)-1 $ (what happens here?)

I´m a bit worried about this induction thing, because I´ve been trying to solve the homework problems for three days with very little progress. If anyone could help me with this problem I would be really grateful.

One more thing, does anyone know any good book which would have mathematical induction for dummies?

All help is appreciated very much.