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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. 1 (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 7-1 X for some k> 1. X - 7 = 7* 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 E N. 1 (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 7-1 X for some k> 1. X - 7 = 7* X , as required.

Database System Concepts
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
Problem 1PE
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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.
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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