How do I approach this question?
How do I approach this question? 64. a) Find an N such that 1 n2 –...
2) Prove that 1 + 3n < 4n for all n > 1. /5 Marks/
1. Show that, for every n > 1: n ka n(n + 1)(2n +1) 6 k=1
(2) Prove by induction that for all integers n > 2. Hint: 2n-1-2n2,
n! 5. Let an On+1 <1 for all n. (1Show that an (2) Use (1) to show that {an} decreases. (3) Is {an} convergent?
(5) Use induction to show that Ig(n) <n for all n > 1.
1) Give a combinatorial proof of the following identity (0 <k<n): n2 k ---- = n.29-1 ke=0
Question 1 1 pts To find P(z<2.35), where do you shade? left Oright between
Let (In), and (yn).m-1 be sequences such that Pr – yn| < 1/n for all n. Use the definition of convergence to prove that, if (2n)_1 is convergent, then (Yn)-1 is convergent.
question 5 5. (a) Informally find a positive integer k for which the following is true: 3n + 1 < n2 for all integers n > k-4 (b) Use induction to prove that 3n +1 < n2 for all integers n 2 k. 6. Consider the following interval sets in R: B-4.7, E = (1,5), G = (5,9), M-[3,6]. (a) Find (E × B) U (M × G) and sketch this set in the-y plane. (b) Find (EUM) x (BUG)...
From 6.3-6. For n E N, let W < W<< W2nt be the order statistics of (2n 1) independent draws from Unifl-1 2ra-+1 (1) Find the PDF of W and W2n+1 (2) By symmetry or otherwise, compute EW+