Let C(n) be the constant term in the expansion of (x + 7)". Prove by induction that C(n) = 7" for all n € N. (Induction on n.) The constant term of (x + 7)¹ is 7 eBook Suppose as inductive hypothesis that the constant term of (x + 7)k-1 is 7-1 Then (x + 7) = (x + 7)k-1. X+7 X so its constant term is 7K-1 X for some k> 1. X ·7= 7K X as required.
Let C(n) be the constant term in the expansion of (x + 7)". Prove by induction that C(n) = 7" for all n € N. (Induction on n.) The constant term of (x + 7)¹ is 7 eBook Suppose as inductive hypothesis that the constant term of (x + 7)k-1 is 7-1 Then (x + 7) = (x + 7)k-1. X+7 X so its constant term is 7K-1 X for some k> 1. X ·7= 7K X as required.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let C(n) be the constant term in the expansion of (x + 7)". Prove by induction that C(n) = 7" for all n € N.
(Induction on n.) The constant term of (x + 7)¹ is 7
eBook
Suppose as inductive hypothesis that the constant term of (x + 7)k-1 is 7-1
Then (x + 7) = (x + 7)k-1.
X+7
X
so its constant term is 7K-1
X
for some k> 1.
X
·7= 7K
X
as required.
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