Question

prove that any positive even integer is of the form 2q+2

Answer 1

$\huge\boxed{\underline{\mathcal{\red{A}\green{N}\pink{S}\orange{W}\blue{E}\pink{R}}}}$

$2q + 2 ...(1)$

$As q = 0,1,2,3,4...$

So by putting values

$=> 2(0) + 2$

$=> 0 + 2$

$=> 2$

-----------------

$=> 2(1) + 2$

$=> 2 + 2$

$=> 4$

-----------------

$=> 2(2) + 2$

$=> 4 + 2$

$=> 6$

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$=> 2(11) + 2$

$=> 22 + 2$

$=> 24$

So by putting q value all of the resultant values are even numbers.

Answer 2

$\huge\boxed{\underline{\mathcal{\red{A}\green{N}\pink{S}\orange{W}\blue{E}\pink{R}}}}$

${\bf{\geen{2q+2}}}$

${\bf{\pink{q=0,12,3,4.....}}}$

${\bf{\blue{if q=0}}}$

${\bf{\blue{=2(0)+2}}}$

${\bf{\blue{=2}}}$

______________________________________

${\bf{\red{if q=1}}}$

${\bf{\red{=2(1)+2}}}$

${\bf{\red{=4}}}$

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${\bf{\green{if q=2}}}$

${\bf{\green{=2(2)+2}}}$

${\bf{\green{=6}}}$

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${\bf{\orange{if q=3}}}$

${\bf{\orange{=2(3)+2}}}$

${\bf{\orange{=8}}}$