#ATTENDANCE QUIZ FOR LECTURE 9 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email: hra25@scarletmail.rutgers.edu
#Subject: p9

#Right after finishing watching the lecture but no later than Oct. 6, 2020, 8:00pm

THE NUMBER OF ATTENDANCE QUESTIONS WERE: 5

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

# Question 1: Let a[i] be the i-th digit of your RUID (if it is zero, make it 1). In how many ways can you walk from 0 to 131 using as fundamental steps the set {a[3]. a[5], a[9]}? (28:43)

#A[3]=7
#A[5]=1
#A[9]=7

# 44040818021566980908154415327216241631937244329204418907831960957242343372748800 ways

#Question 2: Is this sequence in OEIS? (36:30)

# A116975

#Question 3: Let f(x) = 1/(1-4x-x^6); (i) Find the coefficient of x^100 in the Taylor expansion of f(x)? (ii) Find the coefficient of x^101 in the Taylor expansion of f(x)? How far is a(101)/a(100) from the real root of 1-4*x-x^6 (41:30)

(i)   411048332990455915104492378532366163275381170780171837436480
(ii) 1644594257296515568488059327938971072084521685469936722570496


#Question 4: In how many ways can a chess king walk from one corner of the chess board to the opposite corner? (50:25)

# 48639 ways

#Question 5: Is this sequence in the OEIS? (56:24)

# A051708