To show that Pk+1 is true, add (2(k+ 1))3 to both sides of Pk. +(2k)³ +(2k +1 23 +43 +63 + ... Completely factor the right-hand side. 23 +43 +63 +...+(2(k+ 1))³ = 2(k+1 = 2(k+1 = 2(k+1 Rewrite the right-hand side in the desired form. ))³ = 2k²(k + 1)² + (2【 k +1 1)²+(2(k+1,)) ],» )²(4(k+1) )²(k² + 4k+ 4 )²(x + 2 23 + 4³ + 6³ + ... + (2(k + 1))³ = 2 (k+ 1)² ( (k+1) + 1)² X + 4( k + 1 2+ ) 1,9 3² ))
To show that Pk+1 is true, add (2(k+ 1))3 to both sides of Pk. +(2k)³ +(2k +1 23 +43 +63 + ... Completely factor the right-hand side. 23 +43 +63 +...+(2(k+ 1))³ = 2(k+1 = 2(k+1 = 2(k+1 Rewrite the right-hand side in the desired form. ))³ = 2k²(k + 1)² + (2【 k +1 1)²+(2(k+1,)) ],» )²(4(k+1) )²(k² + 4k+ 4 )²(x + 2 23 + 4³ + 6³ + ... + (2(k + 1))³ = 2 (k+ 1)² ( (k+1) + 1)² X + 4( k + 1 2+ ) 1,9 3² ))
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![To show that Pk+1 is true, add (2(k+ 1))3 to both sides of Pk.
+(2k)³ +(2k +1
23 +4³ +6³ +
+
6³ + ... + (2k)³ +
Completely factor the right-hand side.
23 + 43 + 6³ + ... + (2(k + 1))³ = 2( k +1
2k+1
2 k +1
Rewrite the right-hand side in the desired form.
3
))³ = 2k²(k + 1)² + (2k + 1
)²( 4 (k+1)
) ² (k² + 4k +4
)²(x + 2
23 + 4³ + 6³ + ... + (2(k + 1))³ = 2 (k+ 1)² ( (k+ 1) + 1)²
X
2+
4k+1
)
. ))³
2
)²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9f36f111-f1bc-4b8c-9508-d8f50a3e95e1%2Fceaca88b-c85a-48d4-8ed8-763f7d99cac4%2F1k9t9xj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:To show that Pk+1 is true, add (2(k+ 1))3 to both sides of Pk.
+(2k)³ +(2k +1
23 +4³ +6³ +
+
6³ + ... + (2k)³ +
Completely factor the right-hand side.
23 + 43 + 6³ + ... + (2(k + 1))³ = 2( k +1
2k+1
2 k +1
Rewrite the right-hand side in the desired form.
3
))³ = 2k²(k + 1)² + (2k + 1
)²( 4 (k+1)
) ² (k² + 4k +4
)²(x + 2
23 + 4³ + 6³ + ... + (2(k + 1))³ = 2 (k+ 1)² ( (k+ 1) + 1)²
X
2+
4k+1
)
. ))³
2
)²
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