#ATTENDANCE QUIZ FOR LECTURE 16 of Dr. Z.'s Math454(02) Rutgers University


# Please Edit this .txt page with Answers


#Email  ShaloshBEkhad@gmail.com 
#Subject: p16
#with an attachment called
#p16FirstLast.txt
#(e.g. p16DoronZeilberger.txt)


#Right after finishing watching the lecture but no later than Oct. 30, 2020, 8:00pm




THE NUMBER OF ATTENDANCE QUESTIONS WERE:


PLEASE LIST ALL THE QUESTIONS FOLLOWED, AFTER EACH, BY THE ANSWER


1. Convert the following recurrence to explicit form


6*f(n) + 12*f(n+1) + 18*f(n+3) = 0 


A: -(6*f(2)*_R^2 + 4*_R^2 + 12*_R + 6)*(1/_R)^n/((5*_R^2 + 8*_R)*_R)


2. Find f(5) and f(6) 


A: f(5) 
2*I*(f(1)*sqrt(3)/4 - 3*I*f(1)/4 + sqrt(3)/2 - I/2)*(3/2 + sqrt(3)*I/2)^5/3 + 2*I*(-f(1)*sqrt(3)/4 - 3*I*f(1)/4 - sqrt(3)/2 - I/2)*(3/2 - sqrt(3)*I/2)^5/3


f(6)
2*I*(f(1)*sqrt(3)/4 - 3*I*f(1)/4 + sqrt(3)/2 - I/2)*(3/2 + sqrt(3)*I/2)^6/3 + 2*I*(-f(1)*sqrt(3)/4 - 3*I*f(1)/4 - sqrt(3)/2 - I/2)*(3/2 - sqrt(3)*I/2)^6/3


3. What is F(10^6)? How long did it take? What is f(10^6)?


A: 
617.57 seconds - a very large number 


4. Consider the sequence that is defined by the recurrence f(n+1000) =f(n+999) + 5*f(n). What is the ope (N) such that ope (N) f(n) = 0 ?
5. Characterize the sequences that satisfy a homogenous recurrence of order zero. 
the total degree of each term is the same, so there is no constant term 
The expression for a(n) is from a(n-1) to a(n). 
6. Can you prove that d(n)/n! -->1/e 
Yes you can prove this graphically as d(n)/n! Approaches 1/e asymptotically 
7. What is the OEIS number of this sequence? 
A000085
8. Look up the syntax of ZeilbergerRecurrence 
LT(n,k)=G(n,k+1)−G(n,k).