proof by induction

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$$ prove by induction that f(n) = n^3 + 3n^2 +8n is divisible by 6 for all integers n $$

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cremegg [Anki enjoyer]

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@thin wagon

Why are there no spaces

[thin wagon]

Heyyyy

[merry cave]

you put everything in the $$

[thin wagon]

Put ur $$ in front of the text

Just round the equation

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Oh

Am I not supposed to do that

[thin wagon]

no

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sorry

[merry cave]

prove by induction that $f(n) = n^3 + 3n^2 +8n$ is divisible by 6 for all integers n

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val

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cheers

[merry cave]

you done the basis step where n=1?

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ye

ive done step 2 aswell

[merry cave]

then you gotta do n=k+1

[thin wagon]

that’s a solution

[urban egret]

Womp womp

Use strong induction

3 lines

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i see where i went wrong

i didnt look for the k term

[thin wagon]

shhhhh

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i rememebr now

thank you nola

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how

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dw

[urban egret]

Assume true for 1<=m<=k for some m,k in the set of positive integers 👀

[thin wagon]

not fm spec

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so i cant use it?

[urban egret]

You can but it’s not taught

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hmm

[thin wagon]

it’s too complicated if u r not like done w fm

it can be an extra thing

but there’s no point to u learning it

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david stop griefing me

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i see

[urban egret]

Joe Biden

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you know that bit at the end of step 3

do you just have to like know that

[thin wagon]

what

line 3?

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one has to be divisible by 2

[thin wagon]

no one has to be divisible by 2

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oops

meant to put 2

[thin wagon]

because k is an integer and you’re adding an even number onto one and an odd onto the other

regardless of whether k is even or odd

one of those will be even

hence divisible by 2

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oh i see

[urban egret]

Nola so smart

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yes

very clever

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the p bit

can you use any letter

[thin wagon]

yeah

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i see

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the (k+1)(K+4) bit was wrong

i had to factorise 3k^2 + 9k

😢

[thin wagon]

There’s several methods

It’s the same principle though isn’t it

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like it dosent factorise to that

[thin wagon]

I know…

But you have to understand

What they’re doing

Is basically leaving out the 12 as it’s divisible by 6

And then factorising 3k^2 + 9k to 3k(k+3)

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,w (k+1) (k+4)

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Requested by cremegg

[thin wagon]

And then saying one of k, k+3 is divisible by 2 yeah

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oh my teacher just said its wrong as it dosent factor to that

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i see

[thin wagon]

Oh oops LOL wel maybe that’s a mistake

But the method is the same

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okay thanks

[thin wagon]

Y u getting ne to do ur hw for u tho

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i tried it multiple times

but id idnt get the asnwer

so i wanted to see how to answer it

[thin wagon]

lolll ok u should for sure check my method then

I got my negatives mixed up

Tho the principle is exactly the same

So dw

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im not complaining at you btw

[thin wagon]

all it is is you say 12 is divisible by 6

Then the same odd even thing is to watch out for

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sorry if it sounds like it

[thin wagon]

No it’s ok

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alr

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Just remember the odd even thing

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ye

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Cos it comes in handy

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ye

thats the problem i find with proof

i never think about things like that

[thin wagon]

You’ll get used to it with time

Sorry for my mistake