Question: Prove the following proposition using mathematical induction: Pn1 i=0 2 i = 2 n 1 Prove that a + b is an odd integer if

Prove the following proposition using mathematical induction: Pn1 i=0 2 i = 2 n 1

Prove that a + b is an odd integer if and only if a and b are not both odd or both even integers. (Hint: an integer n is even if and only if it equals 2k for some integer k and odd if and only if it equals 2k + 1 for some integer k.)

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