Let C(n) be the constant term in the expansion of (x + 7)". Prove by induction that C(n) = 7 for all n E N. (Induction on n.) The constant term of (x + 7)¹ is = 7⁰ Suppose as inductive hypothesis that the constant term of (x + 7)k-1 is Then (x + 7) = (x + 7)k-1. so its constant term is for some k > 1. -7= as required.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Let C(n) be the constant term in the expansion of (x + 7)". Prove by induction that C(n)
(Induction on n.) The constant term of (x + 7)¹ is
= 74
Suppose as inductive hypothesis that the constant term of (x + 7)k-1 is
Then (x + 7) = (x + 7)k-1.
so its constant term is
=
7 for all nEN.
for some k > 1.
.7 =
1
as required.
Transcribed Image Text:Let C(n) be the constant term in the expansion of (x + 7)". Prove by induction that C(n) (Induction on n.) The constant term of (x + 7)¹ is = 74 Suppose as inductive hypothesis that the constant term of (x + 7)k-1 is Then (x + 7) = (x + 7)k-1. so its constant term is = 7 for all nEN. for some k > 1. .7 = 1 as required.
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