Answer: Find the mistakes in the proof fragments in 3335
Chapter 5, Problem 34(choose chapter or problem)
Theorem: For any integer n ≥ 0,
\(1 + 2 + 2^{2} +· · ·+2^{n} = 2^{n +1} − 1\)
“Proof (by mathematical induction): Let the property P(n) be \(1 + 2 + 2^{2} +· · ·+2^{n} = 2^{n +1} − 1\). Show that P(0) is true: The left-hand side of P(0) is \(1 + 2 + 2^{2} +· · ·+2^{0} = 1\) and the right-hand side is \(2^{0}+1 − 1 = 2 − 1 = 1\) also. So P(0) is true.”
Text Transcription:
1 + 2 + 2^{2} +· · ·+2^{n} = 2^{n +1} − 1
1 + 2 + 2^{2} +· · ·+2^{0} = 1
2^{0}+1 − 1 = 2 − 1 = 1
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