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10-06-2020
Mathematics

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Prove that (2n+1)^2 - (2n+1)^2 is a multiple of 8 for all positive integer values of n

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19biniasztear 19biniasztear

10-06-2020

Answer:

(2n + 1)[(2n + 1) � 1]

(2n + 1)(2n + 1 � 1)

(2n + 1)(2n), or 2n(2n + 1)

2n is an EVEN NUMBER, and adding 1 to an even number creates an ODD number

Therefore, 2n(2n+1)=EVEN NUMBER ODD NUMBER=EVEN NUMBER

Step-by-step explanation:

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