CS 1050 B: Constructing Proofs February 6, 2009
Homework 4
Lecturer: Sasha Boldyreva Due: N/A
Problem 4.1 In the questions below find a recurrence relation with initial condition(s)
satisfied by the sequence. Assume a0is the first term of the sequence.
(a) an= 2n+ 1
(b) an= (−1)n
Problem 4.2 Suppose inflation continues at three percent annually. (That is, an item
that costs $1.00 now will cost $1.03 next year.) Let an= the value (that is, the purchasing
power) of one dollar after n years.
(a) Find a recurrence relation for an.
(b) What is the value of $1.00 after 20 years?
(c) What is the value of $1.00 after 80 years?
(d) If inflation were to continue at ten percent annually, find the value of $1.00 after 20
years.
(e) If inflation were to continue at ten percent annually, find the value of $1.00 after 80 years.
Problem 4.3 In the questions below solve the recurrence relation by discovering a pat-
tern formed by the terms.
an=−10an−1−21an−2, a0= 2, a1= 1
Problem 4.4, 10 points. Problems 28a, 28b, 28c, 28d from Section 7.3 of Rosens
textbook.