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May 28th, 2018, 09:54 PM   #1
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Joined: May 2018
From: Seoul

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recurrence formula problem

how to solve it?

a0=a1=1

thank you!!
Attached Images 1527565739558.jpg (60.5 KB, 16 views) May 29th, 2018, 02:21 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,921 Thanks: 2203 Why do you need to "solve" this? Have you realized that you can deal with the numerator and denominator separately? The denominator leads to $n$ factorial. May 29th, 2018, 12:23 PM #3 Senior Member   Joined: Sep 2016 From: USA Posts: 635 Thanks: 401 Math Focus: Dynamical systems, analytic function theory, numerics What do you mean by "solve"? My guess from your screenshot is that you are solving a linear ODE by power series expansion. The resulting power series described by the recurrence IS the solution. What more could you ask for? June 18th, 2018, 06:06 AM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 You have a formula that says that $\displaystyle a_{n+2}= -\frac{3n+2}{(n+1)(n+2)}a_n$. You are also told that $\displaystyle a_0= a_1= 1$ so $\displaystyle a_2= a_{0+2}= -\frac{3(0)+ 2}{(0+1)(0+2)}(1)= -1$, $\displaystyle a_3= a_{1+ 2}= -\frac{3(1)+ 2}{(1+1)(1+ 2)}(1)= -\frac{5}{6}$, $\displaystyle a_4= a_{2+ 2}= -\frac{3(2)+ 1}{(2+ 1)(2+ 2)}(-1)= \frac{7}{12}$, $\displaystyle a_5= a_{3+ 2}= -\frac{3(3)+ 1}{(3+1)(3+ 2)}\left(-\frac{5}{6}\right)= \frac{5}{12}$, etc. I don't see that giving any reasonable general formula. What is the exact statement of the problem? Tags formula, problem, recurrence Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post riovelo Algebra 4 November 7th, 2016 07:09 AM cnx42 Math 3 May 5th, 2015 07:21 PM boy15 Number Theory 0 August 31st, 2010 08:26 PM Boballoo Computer Science 2 March 23rd, 2010 02:39 PM KranImpire Algebra 5 March 9th, 2010 07:49 PM

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