Suppose we have a recursive sequence J1,. For the purposes of this problem, it does not matter exactly how the fi are defined, only that they are recursively defined. For integer n ≥ 1, let P(n) be the predicate that i=1 fi = 2fn+2 - 3. Don't worry about whether this predicate "makes sense"; we haven't defined the fi so you won't be able to "make sense" of the P(n). It's not important for this problem. Consider a proof by induction that Vn ≥ 1: P(n). Suppose we've gotten to the inductive step, and suppose that the first steps of the inductive sten are

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
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Suppose we have a recursive sequence f1, f2, f3, . . ..
For the purposes of this problem, it does not matter exactly how the f; are defined,
only that they are recursively defined.
For integer n ≥ 1, let P(n) be the predicate that Σi-1 fi = 2ƒn+2 − 3.
Don't worry about whether this predicate "makes sense"; we haven't defined the fi
so you won't be able to "make sense" of the P(n). It's not important for this
problem.
Consider a proof by induction that Vn ≥ 1: P(n).
Suppose we've gotten to the inductive step, and suppose that the first steps of the
inductive step are
Σfi = fk+1 + Σi=₁ fi
= fk + fk-1 + Σk=₁ fi
True or false: Based on the information given, we will need strong induction for this
proof.
True
False
Transcribed Image Text:Suppose we have a recursive sequence f1, f2, f3, . . .. For the purposes of this problem, it does not matter exactly how the f; are defined, only that they are recursively defined. For integer n ≥ 1, let P(n) be the predicate that Σi-1 fi = 2ƒn+2 − 3. Don't worry about whether this predicate "makes sense"; we haven't defined the fi so you won't be able to "make sense" of the P(n). It's not important for this problem. Consider a proof by induction that Vn ≥ 1: P(n). Suppose we've gotten to the inductive step, and suppose that the first steps of the inductive step are Σfi = fk+1 + Σi=₁ fi = fk + fk-1 + Σk=₁ fi True or false: Based on the information given, we will need strong induction for this proof. True False
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