My Math Forum  

Go Back   My Math Forum > College Math Forum > Real Analysis

Real Analysis Real Analysis Math Forum


Reply
 
LinkBack Thread Tools Display Modes
October 8th, 2010, 10:19 AM   #1
Global Moderator
 
The Chaz's Avatar
 
Joined: Nov 2009
From: Northwest Arkansas

Posts: 2,766
Thanks: 4

Infinite series sum

sum
n = 1 to infinity, of
F(n) 2^n
Where F(n) is the n-th Fibonacci number. 1, 1, 2, 3, 5, ...

While trying to help someone else solve this, I realized that I couldn't do it! I also realized that I don't know how to write that in Latex, which sucks because I spent 2.5 hours downloading and 2 Gigs of memory to get that software...

So far I've found that it converges by the ratio test...
"L" is .5*phi
But that doesn't get me any closer to evaluating it!
The Chaz is offline  
 
October 8th, 2010, 11:36 AM   #2
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: Infinite series sum

Pari gives a very suggestive answer. You may be able to take the answer and prove that it's correct.
Code:
suminf(n=1,fibonacci(n)/2^n)
CRGreathouse is offline  
October 8th, 2010, 11:39 AM   #3
Global Moderator
 
The Chaz's Avatar
 
Joined: Nov 2009
From: Northwest Arkansas

Posts: 2,766
Thanks: 4

Re: Infinite series sum

For some reason, it didn't show up in my browser! I'm running OSX
The Chaz is offline  
October 8th, 2010, 11:41 AM   #4
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: Infinite series sum

"it"?
CRGreathouse is offline  
October 8th, 2010, 11:44 AM   #5
Global Moderator
 
The Chaz's Avatar
 
Joined: Nov 2009
From: Northwest Arkansas

Posts: 2,766
Thanks: 4

Re: Infinite series sum

Yeah, you know... THE (approximate) ANSWER!
Please don't make me download pari just to crunch this number. If it weren't for my formatting problems with wolfram I'd be done already





edit.
2.
The Chaz is offline  
October 8th, 2010, 03:57 PM   #6
Math Team
 
Joined: Apr 2010

Posts: 2,780
Thanks: 361

Re: Infinite series sum

Hi The Chaz and CRGreathouse,

I made an attempt...





, so



and

so



Hope it's correct and especially that it helps.

Hoempa
Hoempa is offline  
Reply

  My Math Forum > College Math Forum > Real Analysis

Tags
infinite, series, sum



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Infinite series clandarkfire Calculus 6 November 6th, 2011 03:23 AM
Infinite series : 1/r^r Zeefinity Real Analysis 4 August 28th, 2011 11:18 PM
Infinite Series WannaBe Calculus 3 January 7th, 2010 01:27 AM
Infinite series johnny Calculus 1 September 9th, 2009 05:57 AM
Infinite Series Mathforum1000 Abstract Algebra 0 December 31st, 1969 04:00 PM





Copyright © 2019 My Math Forum. All rights reserved.