May 28th, 2018, 09:54 PM  #1 
Newbie Joined: May 2018 From: Seoul Posts: 1 Thanks: 0  recurrence formula problem
how to solve it? a0=a1=1 thank you!! 
May 29th, 2018, 02:21 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,286 Thanks: 1681 
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: 414 Thanks: 228 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: 3,261 Thanks: 894 
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  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
recurrence relation problem  riovelo  Algebra  4  November 7th, 2016 07:09 AM 
Formula problem, Need help.  cnx42  Math  3  May 5th, 2015 07:21 PM 
recurrence formula help  boy15  Number Theory  0  August 31st, 2010 08:26 PM 
have problem  need formula  Boballoo  Computer Science  2  March 23rd, 2010 02:39 PM 
Formula Problem  KranImpire  Algebra  5  March 9th, 2010 07:49 PM 