October 15th, 2019, 03:41 PM  #1 
Newbie Joined: Oct 2019 From: USA Posts: 3 Thanks: 0  Help series
Please help me with the attached problem!

October 15th, 2019, 04:22 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 3,093 Thanks: 1675  did you try using the given hint? 
October 15th, 2019, 04:23 PM  #3 
Senior Member Joined: Sep 2016 From: USA Posts: 683 Thanks: 456 Math Focus: Dynamical systems, analytic function theory, numerics 
Based on the question you are: 1. Too lazy to even bother pretending this isn't just a straight up request to do your homework for you. 2. In a calculus class. 3. So far from understanding the material that you can't even follow the hint which turns the entire problem into a middle school level algebra problem. I can't help but think that (3) is related to (1). Anyway best of luck when retaking the course. 
October 15th, 2019, 05:13 PM  #4 
Newbie Joined: Oct 2019 From: USA Posts: 3 Thanks: 0 
yes!

October 15th, 2019, 06:02 PM  #5 
Math Team Joined: Jul 2011 From: Texas Posts: 3,093 Thanks: 1675  Did you arrive at a solution? To solve the equation ... $a = \dfrac{1}{2}\left(a + \dfrac{2}{a}\right)$ ... for $a$. I'd start by multiplying both sides by $2$ in order to clear the fraction $\dfrac{1}{2}$. Next, I'd find a common denominator to combine $\left(a + \dfrac{2}{a}\right)$ into a single fraction. Give it a go from there and post your working ... 
November 4th, 2019, 10:24 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 21,106 Thanks: 2324 
I've moved this to Algebra. It's a good idea to let us know why you're stuck, especially when a hint has already been provided. For example, did you understand the wording of the problem? Do you know that "sequence" and "series" have different meanings? Each term in the sequence is the average of two positive terms, and is therefore positive. Does that matter? Using the hint given, and multiplying both sides by $2a$ (to clear both fractions), gives $2a^2 = a^2 + 2$, which implies $a^2 = 2$. Now what? 

Tags 
sequences, series, sigma 
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