You are here:

Calculus/Advanced Calculus of One Variable

Advertisement

Expert: - 2/10/2010


Question
Disprove the conjecture

Conjecture: If {|a_n|}_n converges to |A|, then {a_n}_n converges to A

Answer
Not so.  A could be positive.

Let a_n be -1 + 1/n where n goes to infinity.

The |a_n| converges to |1|, for in actuality, a_n converges to -1.
So a_n converges to -1, whcih is not A.

If there was a statment about A being negative, it would be true, but would be too obvious.
It would be just like is -a_n converges to -A, then a_n converges to A.

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Scotto

Expertise

Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

Experience

Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Publications
Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC. Well over 2,000 of them have been in calculus.

Education/Credentials
I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few junior level courses my sophomore year.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

©2012 About.com, a part of The New York Times Company. All rights reserved.