A-level Proof by induction

[plucky hedge]

I’ve done this Q before

I don’t ecen do fm but I reckon I could remember the steps

Could you just give me 5 ish mins

Ok so

For the first step

Prove for n = 1

Meaning dy/dx as normal

I’ll show on whiteboard

Ignore the stuff at bottom that’s my own work

[paper condor]

Deary me

[plucky hedge]

Now prove for n = k

[plucky hedge]

Sorry

[neat tendon]

😭

[plucky hedge]

We’re gonna need a bigger whiteboard for this

Basically second part prove for n = k

So you differentiate again

Which is long

[neat tendon]

long ass q

[plucky hedge]

Bruh

Fuck u

I was on that part

I’m acc so goated for being able to do this Q even tho I literally don’t do fm

[neat tendon]

oh mb i thought u were giving up 😭

[neat tendon]

yh impressive

[plucky hedge]

It’s fun

And ngl it’s not even hard like that

[neat tendon]

exc

its jus more

[plucky hedge]

The actual maths is pretty basic

[neat tendon]

its not that much harder

[pseudo ocean]

u dont prove its true for n=k

ur assuming it is

[plucky hedge]

But you do for n = k+1

[pseudo ocean]

yeah

using that assumption for n=k

[plucky hedge]

When I did it I did it for n = k and then added the k+1 I think

[pseudo ocean]

you said you dont do fm tho

[plucky hedge]

I don’t

[pseudo ocean]

so good job

[paper condor]

Forget the conclusion and all those formalities

And good handwriting etc

[plucky hedge]

I second that

[plucky hedge]

Thanks g

Where does this rank on fm difficulty

Cuz I’m doing it next year in my gap

[pseudo ocean]

piss easy

[paper condor]

1

[plucky hedge]

Assumed so

It was in the fm mock at my school

[paper condor]

Understatement

[plucky hedge]

Only one person got it

Crazy

[paper condor]

I’d say it’s like a 4/10

[pseudo ocean]

the hardest one is probably divisibility proofs

but thats not bad at all

[plucky hedge]

Isn’t literally the underlying basics of proof by induction alwasy n=1 then n=k then n=k+1

[paper condor]

I think it’s basic induction

The polynomial ones

[pseudo ocean]

wdym

[paper condor]

The factorisation questions

[neat tendon]

yeah

[paper condor]

Sometimes u see it

Sometimes u don’t

[pseudo ocean]

with induction?

[neat tendon]

always the same

[pseudo ocean]

never seen that

[paper condor]

The most basic type

[neat tendon]

ive only seen, series, matrices and divisibility rules

[pseudo ocean]

in the edexcel spec they teach matrix proofs divisibility and series

[neat tendon]

yeah

[pseudo ocean]

what does a polynomial one look like

[paper condor]

Not polynomial

Well it is

I meant basic series formula

[pseudo ocean]

oh

light

[paper condor]

When u expand out a summation into a polynomial and then use standard

Usually

[pseudo ocean]

would be nice if it came up in the exam

[paper condor]

But there’s some that I just don’t think of

[drifting latch]

okay wait

so what you did was differentiate when n=k

so that the differntiation is can be n=k+1

[drifting latch]

this is from edexcel core pure paper 2 2023

[pseudo ocean]

well thats just great then

[drifting latch]

that probs why u didnt see it cuz its new

[pseudo ocean]

i'll give it a go tomorrow if i remember

looks interesting

[drifting latch]

the paper is legit hell bro 💀

i'm an A* student and the paper humbled me

[neat tendon]

yeah

[drifting latch]

thanks Gojo Sensei

[vivid quest]

Ooh nice q 😍

[drifting latch]

how do i close this y'all?

[plucky hedge]

You don’t

It stays here forever

[drifting latch]

fr?

then its cool

[vivid quest]

If u close it we die

[pseudo ocean]

damn

[pseudo ocean]

whyd you change the sign

second line

when differentiating the bracket part

[plucky hedge]

Because (blah)coshx differentiates to blahsinhx

Meaning both those things switch

And cuz its product rule you’re adding it

Which is why the co efficient of coshx is now the co efficient of sings

Sinhx

And vice versa

[pseudo ocean]

im confused

blahcoshx would differentiate to blahsinhx + blah' coshx

omds

[neat tendon]

the cosh goes to sinh

and the sinh goes to cosh

[pseudo ocean]

i know why i was so baffed

[neat tendon]

and i swapped it around

[pseudo ocean]

i was treating n as a variable

im so tapped bruv

thats why i started getting lns

[plucky hedge]

Goodluck to people doing it this year can’t wait to see them do proof by induction w integration

[pseudo ocean]

if that comes up

long for me

[plucky hedge]

What’s the hardest fm topic in your pinion

Pinion

Opinion

[vivid quest]

Vectors 😔

[rich tendon]

Good one

[drifting latch]

ABSOLUTELY AGREE

[neat tendon]

yep

[drifting latch]

AND MODELLING DIFFERENTIAL EQUATION

[neat tendon]

at least these r fun tho

[drifting latch]

take that back gojo or i'm cutting you in 1/2 again

[neat tendon]

so we meet again

[neat tendon]

nah solving DEs r so fun

[drifting latch]

solving is alright

[neat tendon]

figuring out the DE can be a pain but once u do it its satisfying

[drifting latch]

but finding what the equation is from the question is pain

[neat tendon]

but its satisfying when u get it

[drifting latch]

what u just said lol

[drifting latch]

yea it does

[neat tendon]

even when i get a vectors q right im still annoying

bc idek if it was right or not

[drifting latch]

today i had the easiest 3d vectors question and i forgot how to do it 💀

[neat tendon]

too much to remember

[drifting latch]

further pure students have it easy

[neat tendon]

im doin fp1 next year

wht did u choose

[drifting latch]

mechanics 💀

[neat tendon]

and?

[drifting latch]

should've done stats

[neat tendon]

wait wht exma board r u

[drifting latch]

FS1 and FM1 edexcel

[neat tendon]

oh sn

im tryna do FP1, FS1

[drifting latch]

not bad

good luck then!

[pseudo ocean]

fs1 is so calm

first few chapters are some more distributions, they're all calm but negative binomial is ass

then theres a bunch of hypo testing and central limit theorem which is basically normal distribution