Prove the following by math. induction. The format of the proof should be as follows: 1) State
Question:
Prove the following by math. induction. The format of the proof should be as follows:
1) State what, statement you are proving (it, should have a variable on which you do induction as a parameter).
2) State the base base(s) and prove them.
3) State the induction hypothesis
4) State and prove the induction step.
(a) Show limit for all n. 2 ?2, 5 n + 9 6 n .
(b) Show that .
(0) Consider a sequence defined as follows: s 0 = l, s 1 = 2 and for n > 2, s n = l + max {s [n/2] ,s [n/2] }
(Recall that [x] is the door of x, that is, largest integer y x, and [x] is the ceiling of x, smallest integer y > x.)
Provo by strong induction that Vn.
and s [n/2] . Which of them are the same and when? What is the relationship among ones that are not the same?