#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
#Attendance answer
#f(n+3)=-(2/3)*f(n+1)-(1/3)*f(n)

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


#Attendance Question 3
#What is F(10^6)? How long did it take?
#What is f(10^6)?
#Attendance answer
#maple could not compute this

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

#Attendance Question 5
#Characterize the sequence(S) that satisfy a (homage.) recurrence of order zero
#Attendance Answer
#f(n+1)=c*f(n) f(1)=c*f(0),f(2)=c*f(1)=c^2*f(0)

#Attendance Question 6
#Can you prove the d(n)n! -> 1/e
#if evaluate d(n)/n! from 1 to 100 then the sequence approaches 1/e


#Attendance Question 7
#What is the OEIS A number of this sequence
#0.5328023938e-1271
#A9532

#Attendance Question 
#Find the operators in N and N^(-1)
#annihilated by w(n)
#N^(-2) *N^2-(n+2)

#Attendance Question 
#SumTools[Hypergeometric]
#Look up the syntax of ZeilbergerRecurrence 
#ZeilbergerRecurrence(T, n, k, f, l..u)
#T-hypergeometric term of n and k
#n-name
#k-name
#f-name of the recurrence function
#l..u-range for k