#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

#Q1: Convert The following Recurrence to explicit Form. 6*f(n)+12*f(n+1)+18*f(n+3)=0

	#A: 6*f(n)+12*f(n+1)+18*f(n+3)=0
	    6*f(n)+12*b1*f(n)+18*b2*b5*b1*f(n)+18*b2*b6(fn)+18*b3*b1*f(n)+16*b4*f(n)=0
	    f(n)(6+12*b1+18*b2*b5*b1+18*b3*b1+18*b2*b6+16*b4)=0? idk if im doing this right


#Q2: Find f(5) and f(6)

	#A: f(n) = 3*f(n-1)-4*f(n-2)
	   f(5) = 3*f(4) - 4*f(3) = 3*-26 - 4*-22 = 166
	   f(6) = 3*f(5) - 4*f(4) = 3*166 - 4*-26 = 602

#Q3:What is F(10^6)? How long did it take?
    What is f(10^6)? How long did it take?

	#A: Both F(10^6) and f(10^6) are to large to get a result of, and therefore cannot find out how long it takes, (both are atleast >10min). (Using rutgers OIT Computer Labs

#Q4: 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 taht ope(N) f(n) = 0

	#A:ope(N) = N^1000-N^999-5

#Q5: Characterize the sequence(s) that satisfy A (homog.) Recurrence of order zero.

	#A:

#Q6: Can you prove that d(n)/n! -> 1/e

	#A:W get that for a deragenemt of n-Elements, we find athat it is equivalnt to

		D(n) = n!sum((-i)^j*(1/j!),i=0..n). WE also find that
	
	   We also get the taylor expansion of e^x around x=-1 as
		
		1/e = n!sum((-i)^j*(1/j!),i=0..infinity)

	  Thus, for D(n), as n approaches infinity, D(n) is relatively equal to 1/e

#Q7: What is the OEIS A number of this sequence(seq(w(n), n=0..40)

	#A: A000085

#Q8: Find the operators in N and N^(-1) annihilated by w(n)

	#A: