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Gent2324

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I understand lines 1 to 2, but after that im confused. the question is asking to find the value of N given the equation on the first line. im confused on how the equaitons on line 3 are equal, and why line 4 = 12(n+1) . i get line 5, but i have no idea whats going on in line 6 and where they got those numbers from, are they grouping both of the equations made out of the first one or are they only considering the 5th line? and why do they make them equal to eachother on the 8th line? thanks
https://imgur.com/a/Jh91eJU

Guarddyyy

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Do you do further maths?

Gent2324

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(Original post by Guarddyyy)
Do you do further maths?

yes i do

Guarddyyy

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For line 3, you are just rearranging the equation on line 2 to get that summation.

For the 4th line, you understand that the summation can be split into the 2 other summations?

Now the summation for 2n, r=1, and sum of the 12, can be written as (2n)(12) = 24n.
The other summation for n-1, r=1 and sum of the 12, can be written as (n-1)(12) = 12n - 12

now 24n - (12n-12) = 24n - 12n + 12 = 12n + 12 = 12(n+1)

Guarddyyy

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What it seems like what they are doing, is grouping all of the sum of a constant, and then sum of a variable together. If I could type this up in TSR it would make my life a whole lot easier...

But I hope this makes sense, if not, lemme know.

Last edited by Guarddyyy; 2 years ago

Gent2324

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(Original post by Guarddyyy)
For line 3, you are just rearranging the equation on line 2 to get that summation.

For the 4th line, you understand that the summation can be split into the 2 other summations?

Now the summation for 2n, r=1, and sum of the 12, can be written as (2n)(12) = 24n.
The other summation for n-1, r=1 and sum of the 12, can be written as (n-1)(12) = 12n - 12

now 24n - (12n-12) = 24n - 12n + 12 = 12n + 12 = 12(n+1)

oh yes about line 3 didnt notice that lol sorry.
ah ok i see so whenever theres just a number instead of an R you just multiply that number by the number ontop of the sigma sign?

for the 4th line i see that but i dont get how it translates into the equation on the next line, when its 2r do i just do the standard 1/2n(n+1) and then multiply it by 2? i think i see how the equation comes into place now so thank you

Guarddyyy

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I'm not 100% sure what you mean by a number instead of r, but for the 4th line (I'm assuming you mean the 2n, r=n and sum 12), it's not in any way connected to line 5 (where it has 2n, r=n and 2r). It seems like the challenge is just breaking down each section by first dealing with the sum of the 12ths then sum of the 2r's.

sweetstars

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(Original post by Gent2324)
I understand lines 1 to 2, but after that im confused. the question is asking to find the value of N given the equation on the first line. im confused on how the equaitons on line 3 are equal, and why line 4 = 12(n+1) . i get line 5, but i have no idea whats going on in line 6 and where they got those numbers from, are they grouping both of the equations made out of the first one or are they only considering the 5th line? and why do they make them equal to eachother on the 8th line? thanks
https://imgur.com/a/Jh91eJU

uhh what is this nonsense? XD what topic is this in further maths? (also is this a-level or gcse?)

Gent2324

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(Original post by sweetstars)
uhh what is this nonsense? XD what topic is this in further maths? (also is this a-level or gcse?)

series, chapter 3, it is a challenge question though so its not all on that difficulty. we did it last term but i forgot it and we've started proof by induction now and i needed to revisit series. and yes its a level. do you do series in gcse?

Guarddyyy

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If you want me to write it up clearer, I can do that for you Gent2324

Gent2324

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#11

(Original post by Guarddyyy)
If you want me to write it up clearer, I can do that for you Gent2324

i get it now so no need to write it up, thank you very much for your help. annoyingly in the solution banks they often group multiples of numbers together without showing how you get them which is a bit annoying...

Guarddyyy

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Yep, summations are definitely the topic I am the worst at...

Gent2324

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(Original post by Guarddyyy)
Yep, summations are definitely the topic I am the worst at...

have you started proof by induction yet? the algebra gets pretty tricky...

Guarddyyy

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Not yet, I am about to move on to volumes of revolution, then I think matrices then proof by induction,

sweetstars

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(Original post by Gent2324)
series, chapter 3, it is a challenge question though so its not all on that difficulty. we did it last term but i forgot it and we've started proof by induction now and i needed to revisit series. and yes its a level. do you do series in gcse?

Thanks for answering. We do it neither in gcse maths or gcse further maths thankfully. I'm already struggling in further maths while everyone whizzes through all those questions. XD Also sorry for commeting something irrelevant, i feel like I'm just unnecessarily filling up your thread.

Gent2324

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(Original post by sweetstars)
Thanks for answering. We do it neither in gcse maths or gcse further maths thankfully. I'm already struggling in further maths while everyone whizzes through all those questions. XD Also sorry for commeting something irrelevant, i feel like I'm just unnecessarily filling up your thread.

no worries, its not ridiculously hard it just looks a bit weird when looking at it for the first time (or the 200th if youre me)

(Original post by Guarddyyy)
Not yet, I am about to move on to volumes of revolution, then I think matrices then proof by induction,

we're starting volumes of revolution but our teacher has had to teach us integration and differentiation first, apparently its easy.
matrices is incredibly easy and so is linear transformations, not complicated at all really. roots of polynomials is fine, loci in the argand diagrams are hell

. proof by induction is easy up until you have to rearrange a quadratic or up to quartic into the given equation. it gets pretty confusing with factorials etc..

Guarddyyy

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(Original post by Gent2324)
no worries, its not ridiculously hard it just looks a bit weird when looking at it for the first time (or the 200th if youre me)

we're starting volumes of revolution but our teacher has had to teach us integration and differentiation first, apparently its easy.
matrices is incredibly easy and so is linear transformations, not complicated at all really. roots of polynomials is fine, loci in the argand diagrams are hell

. proof by induction is easy up until you have to rearrange a quadratic or up to quartic into the given equation. it gets pretty confusing with factorials etc..

I'm about to begin integrating and differentiating trigonometry (because I'm in A2, but I'm doing AS Further Maths).

Gent2324

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(Original post by Guarddyyy)
I'm about to begin integrating and differentiating trigonometry (because I'm in A2, but I'm doing AS Further Maths).

what modules are you doing for fm? i was going to do stats and mechanics but ive started to hate applied maths so we're doing decision and further pure 1 instead

Guarddyyy

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(Original post by Gent2324)
what modules are you doing for fm? i was going to do stats and mechanics but ive started to hate applied maths so we're doing decision and further pure 1 instead

Modules?... urm... all I know is I'm doing pure 1, stats 1 and mechanics 1.