.
Now, , and .
Similarly,
, and .
Thus the above becomes:
.
--Kevin C.
Can someone please help me, I really don't know to do this task. It says it's a Fibonacci sequence. Anyway it could be tommorrow on my exam.
It should be proven by induction.... I'm stuck on third step when n = k + 1.. I don't know what to do...
Help me until tommorrow please....
Thanks in advance...
Thank you, man. You solved it
Only thing is that we're solving induction by these steps:
1° check is the statement True for n = 1
2° assume that the statement is also true for n = k
3° with help of step 2° try to prove that the statement is true for n = k+1
so, I don't want to be rude, this here helps me, but can you explain a bit why this on the beginning:
It's just that I don't know the order of this task you've done, and what should I add, which factors...
Thanks alot man.. You really solved my problems...
Remember the definition of the Fibonacci sequence: That , with initial values , . This is a second-degree difference equation/recurrence relation. You need to prove that your non-recursive formula holds for both those initial values. Then assume that it holds for n=k and n=k-1, and show that the formula fits the recursion relation ; this last step is what I did.
--Kevin C.