What do we need to know in proof by induction?
The whole chapter confuses me quite a lot...is it a matter of just learning off?
Any help would be greatly appreciated, thanks!
yeah its pretty much a matter of learning it of but if you break it down you need to sub in n=1 prove it is true, assume it is true for n=k, then prove true for n=k+1 given n=k is true, final step is to conclude
when you do the proof, you have the equation with (k+1) subbed in for X , what is it then u add onto it before working it out????
usually when you analyse your equation for n=k+1 you will see that it is similar to n=k as there are certain things that they have in common you can then sub in the value for n=k for the values common to n=k+1 and the solve
when you have the answer that you need to get at the end on the right-hand side and you have it equal to a sequence that can end with, for example, 1+2+3+....+k+(k+1). You can then sub the previous 'assumption' answer (from the assume true for n=k part) in for the part of the sequence up until '+k' and then just change it around until you get what you had on the right hand side.