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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.

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.

Advanced Engineering Mathematics
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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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.
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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