an = 1 + 2an-1
a1 = 1
a)Guess what an is based on inspection of this sequence
b) Prove the expression in (a) using induction
edit: ah my subscript got messed up, dunno how to post it on forums
suppose to be a subscript n = 1 + 2a subscript n-1
a subscript 1 = 1
Yes, that is correct. Now, we need to prove that by induction.
Basis: n=1: correct.
Assume that it holds for n (that is, ), and now we need to prove that it is correct for , that is, we need to prove that .
which is what we wanted to prove, therefore the assumption holds for any and we are done.
Thanks mate, that actually makes a lot of sense when i go through it slowly
Just a quick question though, when we went over examples in class we always proved n-1 instead of n+1. Basically if one is true the one before it is true as well. I'm assuming this works the same way.