You are here:

Calculus/sum of all as N goes from 1 to infinity of the function (1/2^n^2)

Advertisement

Expert: - 4/1/2008


Question
I know what the answer is for (1/2^n).  It's simply 1.  But what does it become when you square n?  Also, is there a general formula to figure out what (1/x^n^2) where x can be any integer?

Answer
The answer for 1/k is k/(k+1) if the first term is n=0.  For n=1 and k=2, the sum is 1.

For the following, I took the first term as n=0.

I don't know if there is a formula for it, but calculating the first four terms gives me accuracy out to six decimal places.

It converges as long as |x|>1 since if |x|<1, then 1/x is greater than 1.  If x=1, it progresses on like counting.  If x=-1, it alternates between 1 and 0.

Thank you for the great question and I hope this meets your needs.

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.