Now assume that is true.
Look at the next step.
Can you finish?
I'm not sure what to do with this induction question, can anyone help me please?
Let a_1=0, a_2=3, and, for all n>=3 let
a_n= 1/2(a_(n-1) + a_(n-2))
By induction on n, show that for all n>=2,
a_n= 2 + 4(-1/2)^n.
What I did so far was work with the 2nd equation, and said:
0= 2 + 4(-1/2)^1
= 2 - 2
therefore it is true for n=1
Assume true for n=k
a_k= 2 + 4(-1/2)^k
...what's the next step for the proof?Or have I gone completely wrong from the beginning?? Thanks in advance for your help guys!
Thank you so much all you guys for your help!
One more question , and then I think I'm done with this lot of questions , the end of this question after the induction is:
deduce that (a_n) 2.
What I did so far was:
|a_n- | = |2+4(-1/2)^n-2|
....what do I do from here please? How do I prove 2 is ??