Prove for all natural numbers n if n is odd then n^2 + 3n is even

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asked Feb 26, 2018 163k views

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Siamii · Answer 1 · 2018-03-04T06:26:20+0000

an odd number can be written in the form 2x+1.

(2x+1)(2x+1)+3(2x+1) =
4x²+4x+1+6x+3=
4x² + 10x +4

now 4x² is even because 4 is a multiple of 2
10x is even because 10 is a multiple of 2
4 is even

add 3 evens together and you get yet another even

Prove for all natural numbers n if n is odd then n^2 + 3n is even

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