1.2 #2 2 Prove 1³ +2³+ ... +N³ = [ ½/2N (N+1)]² for all NEN show N=1 1³= 1 [1/2₂ (1) (1 +D]² >> ½/2₂ (2) → ¾/2=1 2 Assume KEN Apply Yht! 3 1³ +2³² + ... + K³ = [ ½/2₂K (K+D]² 13³ +2³3 + ... + K³ + (K+1) ³ = [ ½/₂K(K+1)] ² + (K+1) = [ ½/₂(K+1)K]²+ (K+1) 2 [ ½/2[h+1)(h+z)] ²

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,...
icon
Related questions
Question
1.2 #2
3
Prove 1³ +2³+ ... +N³ = [ ½/₂2N (N+1)] ² for all NEN
7
1³= 1 [1/2₂ (0 (1+0] ² > ½/2 (2) → ²/2 = 1 ✓
show N=1
2 Assume KEN
Apply +1
1³ +2³+ ... + K³ = [ ½/₂K/K+D]²
2
13 +2²³ + ... + K³ + (k+1) ³ = [ ½/₂K(K+1)] ² + (+1)
= [ ½/₂2(K+1)K] ² + (K+1)
2
[ ¼/2₂ (h+1)(h+z)]²
Transcribed Image Text:1.2 #2 3 Prove 1³ +2³+ ... +N³ = [ ½/₂2N (N+1)] ² for all NEN 7 1³= 1 [1/2₂ (0 (1+0] ² > ½/2 (2) → ²/2 = 1 ✓ show N=1 2 Assume KEN Apply +1 1³ +2³+ ... + K³ = [ ½/₂K/K+D]² 2 13 +2²³ + ... + K³ + (k+1) ³ = [ ½/₂K(K+1)] ² + (+1) = [ ½/₂2(K+1)K] ² + (K+1) 2 [ ¼/2₂ (h+1)(h+z)]²
Expert Solution
steps

Step by step

Solved in 3 steps with 16 images

Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education