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what is 2(3) ?

2n(2n+1) = 2(2n^2+n) = 2k for some integer k

Idk if that's the answer

what is 2(3) ?

I'm kinda confused on this question

then you should determine what it means to be even and odd ...

and maybe what it means to calculate a product

I think it makes an even number like for example it says 3*6=18
5*12=60

your assumption is good,
2 (3) = 6
even (odd) even
works out in trials

in general, i already posted the proofing

Ima go with even

|dw:1440477601372:dw|
@amistre64 is there a special reason you used 2n?

n is a number, even or odd
the set of even numbers is: 2n
the set of odd numbers is: 2n+1

n(n+1) is just a special case and not a generalization
2(7) does not fit

i spose i shoulda used i different variable as well ... n_1 and n_2 maybe

\[2n_1(2n_2+1)=2k\]

it didn't make a difference to me n is just a number see above agree result still even

if n is even then n + 1 is odd
if n is odd then n + 1 is even

n(n+1) is a special case of even times odd,

how do we prove its good for all cases?
2(7) is not of the form: n(n+1) is it?

do you agree odd*odd is always odd and even *even is always even?

ok thanks

youre welcome