b) Is it possible to formulate a conjecture about the units digit of numbers of the form 7^2 - 2^n, where n is a natural number? If so, formulate a conjecture in the form of a conditional statement in the form “If n is a natural number, then : : :
b) Is it possible to formulate a conjecture about the units digit of numbers of the form 7^2 - 2^n, where n is a natural number? If so, formulate a conjecture in the form of a conditional statement in the form “If n is a natural number, then : : :
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 49E: Show that if the statement
is assumed to be true for , then it can be proved to be true for . Is...
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Please answer question b.
b) Is it possible to formulate a conjecture about the units digit of numbers
of the form 7^2 - 2^n, where n is a natural number? If so, formulate a
conjecture in the form of a conditional statement in the form “If n is a
natural number, then : : :
Transcribed Image Text:10. Exploring Propositions. In Progress Check 1.2, we used exploration to
show that certain statements were false and to make conjectures that certain
statements were true. We can also use exploration to formulate a conjecture
that we believe to be true. For example, if we calculate successive powers of
2 (2', 22, 23, 2ª, 25, ...) and examine the units digits of these numbers, we
could make the following conjectures (among others):
000
BY NC SA
16
Chapter 1. Introduction to Writing Proofs in Mathematics
• If n is a natural number, then the units digit of 2" must be 2, 4, 6, or 8.
• The units digits of the successive powers of 2 repeat according to the
pattern "2, 4, 8, 6."
(a) Is it possible to formulate a conjecture about the units digits of succes-
sive powers of 4 (4', 4², 4³, 4ª, 45, . )? If so, formulate at least one
conjecture.
(b) Is it possible to formulate a conjecture about the units digit of numbers
of the form 7" – 2", where n is a natural number? If so, formulate a
conjecture in the form of a conditional statement in the form "If n is a
natural number, then ... ."
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