Any sum of two or more integers is a result of successive additions of two integers at a

Chapter 5, Problem 15

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Any sum of two or more integers is a result of successive additions of two integers at a time. For instance, here are a few of the ways in which \(a_{1} + a_{2} + a_{3} + a_{4}\) might be computed: \((a_{1} + a_{2}) + (a_{3} + a_{4})\) or \(((a_{1} + a_{2}) + a_{3}) + a_{4})\) or \(a_{1} + ((a_{2} + a_{3}) + a_{4})\). Use strong mathematical induction to prove that any sum of two or more even integers is even.

Text Transcription:

a_1 + a_2 + a_3 + a_4

(a_1 + a_2) + (a_3 + a_4)

((a_1 + a_2) + a_3) + a_4)

a_1 + ((a_2 + a_3) + a_4)

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