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
May 11th, 2007, 08:07 AM   #1
Newbie
 
Joined: May 2007

Posts: 1
Thanks: 0

Power Series and Sequences!!!

Hi all!!

I am currently taking a Laplace Transforms and Fourier Series class, and have no idea where to start in this particular problem...

Use power series to find a formula for the sequence

a sub 0 = 1 a sub 1 = 1, a sub (n+2) - 4a sub (n+1) + 4a sub n = 0

Any help is much appreciated!!!!
ecsu103 is offline  
 
May 13th, 2007, 06:59 PM   #2
Site Founder
 
julien's Avatar
 
Joined: Nov 2006
From: France

Posts: 824
Thanks: 7

This is a linear recurrence with constant coefficients, which you know how to solve explicitly (using the Kernel's lemma from linear algebra).

If you want to use power series (which seems to be asked here), you need to find a function y(t) such that y(0)=1, y'(0)=1 and y^(2n+2)=4y^(n+1)-4y^(n).Taking n=0 gives a necessary condition for y to exist, and determines such an y uniquely. The power series development of this solution y will be a candidate, but you'll still have to verify that it satisfies the required conditions.

I let you solve all of this numerically.
julien is offline  
May 14th, 2007, 02:37 AM   #3
Senior Member
 
Joined: Nov 2006
From: I'm a figment of my own imagination :?

Posts: 848
Thanks: 0

Have you learned about Binet's formula for the fibonacci sequence? Specifically about how it was derived? This would give you another way to give a formula in closed form for the recurrence.
roadnottaken is offline  
Reply

  My Math Forum > College Math Forum > Real Analysis

Tags
power, sequences, series



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
In need of help disk, series test, taylor, and power series g0bearmon Real Analysis 2 May 22nd, 2012 12:10 PM
Sequences and Series - Natural Number Series bilano99 Algebra 4 October 28th, 2011 07:09 AM
sequences and series: geometric series cindyyo Algebra 2 August 24th, 2008 01:25 AM
sequences and series: Arithmetic Sequences cindyyo Algebra 2 August 20th, 2008 02:40 AM
In need of help disk, series test, taylor, and power series g0bearmon Calculus 1 December 31st, 1969 04:00 PM





Copyright © 2019 My Math Forum. All rights reserved.