ANOTHER MATHS ExTENSION QUESTION (1 Viewer)

[super.muppy]

yea sorry but im new to this extension stuff so im noob but i really tried
anyways:
Use mathematical induction to prove that for all positive integers n:
(a) 1^2+2^2+3^2+...+ N^2 = (1/6)n(n+1)(2n+1)
show working and plz briefly explain thanks to whoever dat tries

 

[super.muppy]

plz

 

[jordankuai22]

plz

no, fuck off

 

[TBK11]

no, fuck off

seconded

..lol Super Muppy

ill say this once more if your didn't read my previous post

"""""""CALM THE FUCK DOWN""""""

Its holidays Get out enjoy your self stop doing this nonsense Extension crap honestly
sorry if i offended you but ya

 

[super.muppy]

lols coming from a guy who pulled a whole nighter

 

[suzlee]

lols coming from a guy who pulled a whole nighter

HAHAHAHA

yeah :uhhuh:



That's NEVER going to die.
We'll be thinking back to that old legend in our HSC year, I promise you...

 

[kurt.physics]

1² + 2² + 3² +...+ n² = [n(n + 1)(2n + 1)] ÷ 6

First we see if its true for the most simplest case, n = 1

RHS = 1(1 + 1)(2 + 1) ÷ 6 = (1 * 2 * 3) ÷ 6 = 6 ÷ 6 = 1 = 1² = LHS

Then we assume its true for n = k. ie

1² + 2² + 3² +...+ k² = [k(k + 1)(2k + 1)] ÷ 6

Now we prove its true for n = k + 1. ie

1² + 2² + 3² +...+ k² + (k + 1)² = [(k + 1)(k + 2)(2(k + 1) + 1)] ÷ 6

LHS = 1² + 2² + 3² +...+ k² + (k + 1)²

Because we made the previous statement, we can sub this in to the k + 1 equation to see if it holds.

= ( [k(k + 1)(2k + 1)] ÷ 6 ) + (k + 1)²

= ( k(k + 1)(2k + 1) + 6(k + 1)² ) ÷ 6 (making as one fraction)

= ( (k + 1)[ k(2k + 1) + 6(k + 1)] ) ÷ 6 (factoring k + 1)

= ( (k + 1)[ 2k² + 7k + 6] ) ÷ 6

= ( (k + 1)(k + 2)(2k + 3) ) ÷ 6 (factoring 2k² + 7k + 6 [check yourself if you like])

=RHS (this can be show by subing the k + 1 into the original formula)

Then you write a conclusive statement like; we have shown this to be true for k + 1, therefore it is true for all integers. Or whatever (i dont have textbook beside me)

Thats it

 

[vongSTAA]

You know School Certificate has finished already right? lmao.

Year 11 won't come for another 3 months, chillax.

 

[TBK11]

lols coming from a guy who pulled a whole nighter

yes.. and im proud of my efforts but this is yr10 and ur doin yr11 stuff calm it chillax hang out with your friends (if you have any) watch movies play ping pong enjoy your self jus plz dont do any work lol this is the longest break we'll get make the most of it my friend

 

[Aznmichael92]

yes.. and im proud of my efforts but this is yr10 and ur doin yr11 stuff calm it chillax hang out with your friends (if you have any) watch movies play ping pong enjoy your self jus plz dont do any work lol this is the longest break we'll get make the most of it my friend

i dont think there is anything wrong with doing a bit of year 11 before hand. It gives you a head start for next year so you wouldn't have to study as much. You either take your break now or later.

 

[TBK11]

i dont think there is anything wrong with doing a bit of year 11 before hand. It gives you a head start for next year so you wouldn't have to study as much. You either take your break now or later.

True but you don't want to look back at your life and go "oh god i spent my holidays studying for next yr i never did anything worth while"
has happened to a few people that i know they regret not enjoying there holidays
but yeh preparing for the year ahead is ok but right now a lil bit early dont.ya.think

 

[lyounamu]

yea sorry but im new to this extension stuff so im noob but i really tried
anyways:
Use mathematical induction to prove that for all positive integers n:
(a) 1^2+2^2+3^2+...+ N^2 = (1/6)n(n+1)(2n+1)
show working and plz briefly explain thanks to whoever dat tries

When you post up a year 11 to year 12 level question go to maths forum. People in this forum will basically have no idea (most of them).

 

[youngminii]

Year 11 is nothing.
But then I suppose studying can't hurt

Also, kurt physics wthell O.O You're too smart for your age

 

[supercalamari]

HAHAHAHA

yeah :uhhuh:



That's NEVER going to die.
We'll be thinking back to that old legend in our HSC year, I promise you...

I'm still of the opinion that we need pics or it didn't happen, but TBK, I agree with suzlee

 

[TBK11]

I'm still of the opinion that we need pics or it didn't happen, but TBK, I agree with suzlee

pics errr you should have asked before i burnt all that shit everything related to yr10 burnt it all and made me so happy =]

 

[victoria10]

what the fuck is all that?

my god calm the fuck down!


exams are over, this is bludge time not study time!

 

[studentcheese]

Some people are accelerating in Maths.

 

[youngminii]

I'm still of the opinion that we need pics or it didn't happen, but TBK, I agree with suzlee

/b/ is for over 18 year olds.. Gtfo my /b/

 

[supercalamari]

So you are either a really old year 11 student or a hypocrite? Ok cool. Gtfo my year ten forum

 

[youngminii]

So you are either a really old year 11 student or a hypocrite? Ok cool. Gtfo my year ten forum

Ouch