Let C(n) be the constant term in the expansion of (x + 6). Prove by induction that C(n) = 6 for all n E N. (Induction on n.) The constant term of (x + 6)¹ is Suppose as inductive hypothesis that the constant term of (x + 6)k-1 is Then (x + 6) = (x + 6)k-1. so its constant term is for some k> 1. 6 = as required.
Let C(n) be the constant term in the expansion of (x + 6). Prove by induction that C(n) = 6 for all n E N. (Induction on n.) The constant term of (x + 6)¹ is Suppose as inductive hypothesis that the constant term of (x + 6)k-1 is Then (x + 6) = (x + 6)k-1. so its constant term is for some k> 1. 6 = as required.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 49E
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![Let C(n) be the constant term in the expansion of (x + 6)". Prove by induction that C(n) = 6" for all n E N.
(Induction on n.) The constant term of (x + 6)¹ is
Suppose as inductive hypothesis that the constant term of (x + 6)k-1 is
Then (x + 6) = (x + 6)k −1 .
so its constant term is
for some k > 1.
.6=
, as required.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49655a96-3dec-4fd2-a317-d4fff3ba2079%2F730e5f3a-a9b1-4094-a9f6-35fa28a5fbff%2Fxsq6m_processed.png&w=3840&q=75)
Transcribed Image Text:Let C(n) be the constant term in the expansion of (x + 6)". Prove by induction that C(n) = 6" for all n E N.
(Induction on n.) The constant term of (x + 6)¹ is
Suppose as inductive hypothesis that the constant term of (x + 6)k-1 is
Then (x + 6) = (x + 6)k −1 .
so its constant term is
for some k > 1.
.6=
, as required.
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