Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
moneybird
Group Title
Suppse that \[f(n)=2n\lfloor \frac{1+\sqrt{8n7}}{2} \rfloor\] and \[g(n)=2n\lfloor \frac{1+\sqrt{8n7}}{2} \rfloor\] for each positive integer n.
Suppose that A = {f(1); f(2); f(3); ...} and B = {g(1); g(2); g(3);...}; that is, A is the range of f and B is the range of g. Prove that every positive integer m
is an element of exactly one of A or B.
 2 years ago
 2 years ago
moneybird Group Title
Suppse that \[f(n)=2n\lfloor \frac{1+\sqrt{8n7}}{2} \rfloor\] and \[g(n)=2n\lfloor \frac{1+\sqrt{8n7}}{2} \rfloor\] for each positive integer n. Suppose that A = {f(1); f(2); f(3); ...} and B = {g(1); g(2); g(3);...}; that is, A is the range of f and B is the range of g. Prove that every positive integer m is an element of exactly one of A or B.
 2 years ago
 2 years ago

This Question is Closed

Mr.Math Group TitleBest ResponseYou've already chosen the best response.0
I feel lazy to try it out now, but I have an idea for you that you might want to try. Divide your proof into two parts. i) The first part shows that \(g(n)\ne f(n)\) \(\forall n\in \mathbb{N}\). ii) The second part shows that if \(\forall n\in \mathbb{N}\), \(f(n)\ne m\) for some integer m, then \(\exists n \in \mathbb{N} \) such that \(g(n)=m\).
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.0
i really want to see the solution for this problem :)
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.