2 (i) Show that the result 1+ 5+9 +... + (4n – 3) = n(2n – 1) is true %3D for the casen= 1. (ii) Assume that 1 + 5 + 9 + ...+ (4k – 3) = k(2k – 1) and use this to prove that: 1+5+ ... +(4k – 3) + (4(k + 1) – 3) = (k + 1) (2(k + 1) – 1). %3D (iii) Explain how parts (i) and (ii) together prove that: 1+ 5+9 + ... + (4n – 3) = n(2n – 1)
2 (i) Show that the result 1+ 5+9 +... + (4n – 3) = n(2n – 1) is true %3D for the casen= 1. (ii) Assume that 1 + 5 + 9 + ...+ (4k – 3) = k(2k – 1) and use this to prove that: 1+5+ ... +(4k – 3) + (4(k + 1) – 3) = (k + 1) (2(k + 1) – 1). %3D (iii) Explain how parts (i) and (ii) together prove that: 1+ 5+9 + ... + (4n – 3) = n(2n – 1)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![2
(i)
Show that the result 1+ 5+9 +... + (4n – 3) = n(2n – 1) is true
%3D
for the casen= 1.
(ii) Assume that 1 + 5 + 9 + ...+ (4k – 3) = k(2k – 1)
and use this to prove that:
1+5+ ...
+(4k – 3) + (4(k + 1) – 3) = (k + 1) (2(k + 1) – 1).
%3D
(iii) Explain how parts (i) and (ii) together prove that:
1+ 5+9 + ... + (4n – 3) = n(2n – 1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe2b3852-f7e0-4ebb-b6d4-3228c5608835%2Fa94d3c16-0315-44f1-b103-9d5b4262aac8%2Fffclunf.jpeg&w=3840&q=75)
Transcribed Image Text:2
(i)
Show that the result 1+ 5+9 +... + (4n – 3) = n(2n – 1) is true
%3D
for the casen= 1.
(ii) Assume that 1 + 5 + 9 + ...+ (4k – 3) = k(2k – 1)
and use this to prove that:
1+5+ ...
+(4k – 3) + (4(k + 1) – 3) = (k + 1) (2(k + 1) – 1).
%3D
(iii) Explain how parts (i) and (ii) together prove that:
1+ 5+9 + ... + (4n – 3) = n(2n – 1)
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