i) Given that , where n is an integer, prove that
ii) Hence find In in terms of n.
I can do the first part.
How do i do the second part?
Starting from and calculating subsequent values of using the recurrence equation , we get
As you noted, , which, by definition, is . Further, we note that for odd n and for even n. The sequence shows a similar behavior with respect to alternating signs. Altogether, .