Find the mistakes in the proof fragments,
Exercise
Theorem: For any integer n > 0,
1 + 2 + 22 + … + 2n = 2n +1 –1.
“Proof (by mathematical induction): Let the property
P(n) be 1 + 2 + 22 +…+ 2n = 2n +1 –1.
Show that P(0) is true:
The left-hand side of P (0) is 1 + 2 + 22 + … + 20 = 1 and the right-hand side is20+1 –1 = 2 –1 = 1 also. So P (0) is true.”
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