00:01
Hi, in this question we are asked to show that for a fibonacci sequence, this formula here is true for any positive integer n.
00:14
So the formula says that if we add the odd terms of fibonacci sequence together from 1 up to 2n minus 1, it will equal the event term, the next event term, like f2n.
00:32
So we will prove this using induction on n.
00:35
So let this equation, this statement be p of n.
00:42
And i assume everyone know what fibonacci is.
00:45
We start with 0 and 1.
00:47
And the next term, after that, we'll add the previous two terms.
00:53
Okay, so the best step of the induction, we start with n equal to 2.
01:02
And if we put in p of n, p of n, would say that.
01:08
F1 is equal to f2 which is true because f0 is 0 and f1 is 1 so they add up to 1 so this is f2 f1 f0 all right so best step is clear next for inductive step we suppose that the statement is true for some n we want to show that p of n plus 1 is also true so we have to use p of n as information as our starting point somehow and show that p of n plus 1 is also true...