1.2 #2 3 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 ✓ Assume KEN 3 Apply Pht! 3 1 ³+2 ³+ ... + K³ = [ ½/₂K/K+D]² 1³ +2³+ ... + K³ + (K+1) ³ = [/₂ K (K+1)] ² + (+1) = [/2₂(K+1)K] ² + (K+1) [1/₂2(K+1)(h+2)]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,...
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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
Step 1: Define the problem

To prove :-

1 cubed plus 2 cubed plus............... plus N cubed equals open square brackets 1 half N open parentheses N plus 1 close parentheses close square brackets squared

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