Kenneth Chan
#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
Attendance Question 1
Convert the following recurrence to explicit form
6*f(n)+12*f(n+1)+18*f(n+3)=0 
Answer
6f(n)=-12f(n+1)-18f(n+3)

Attendance Question 2
Find F(5) and F(6)
Answer
F(5)=3f(4)-4f(3)=3(-26)-4(-22)=10
F(6)=3f(5)-4f(4)=3(10)-4(-26)=134

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

Attendance Question 4
Consider the sequence that is defined by the recurrence 
f(n+1000)=f(n+999)+5f(n)
What is the operator ope(N) such that ope(N) f(n)=0
Answer
infinity?

Attendance Question 5
Characterize the sequences that satisfy a (homog.) recurrence of order zero
Answer
they has a degree k with constant coefficients

Attendance Question 6
Can you prove that d(n)/n! ->1/e
Answer
isnt d(n)/n! the combinitoric formula. I do not see where you recieve an e from

Attendance Question 7
What is the OEIs a number of this sequence evalf(w(1000)/1000!)
Answer 
A000085

Attendance Question 8
Find the operators in N and N^(-1) 
annihilated by w(n)
Answer
ope(n,N^-1)

Attendance Question 9
?Sumtools[Hypergeometric]
look up the syntax of ZeilbergerRecurrence 
Answer