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    (Original post by Zacken)
    No, of course not, why would they?
    Wouldnt of thought so but my school were going on and on about how strict they were
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    For step ii 2015 question 5 i've just proved by induction S(n)=arctan(n/(n+1)) for the first bit but then i realised that I should have proved tanS(n)=n/(n+1) for the first bit and S(n)=arctan(n/(n+1)) for the second bit, are they not the same thing? surely if one is true then the other is true? also how would you prove anS(n)=n/(n+1) without using S(n)=arcgan(n/(n+1))? sorry the mark scheme was a bit cryptic so i just asked on here
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    (Original post by porridgepie)
    For step ii 2015 question 5 i've just proved by induction S(n)=arctan(n/(n+1)) for the first bit but then i realised that I should have proved tanS(n)=n/(n+1) for the first bit and S(n)=arctan(n/(n+1)) for the second bit, are they not the same thing? surely if one is true then the other is true? also how would you prove anS(n)=n/(n+1) without using S(n)=arcgan(n/(n+1))? sorry the mark scheme was a bit cryptic so i just asked on here
    Well, no - tan S_n = a and S_n = arctan a are two different things, remember that tangent is a pi-periodic function, so how do you know that it's know S_n = arctan a + pi, for example? You need to prove that S_n is bounded between 0 and pi for you to assert that S_n = arctan a.
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    (Original post by Zacken)
    Well, no - tan S_n = a and S_n = arctan a are two different things, remember that tangent is a pi-periodic function, so how do you know that it's know S_n = arctan a + pi, for example? You need to prove that S_n is bounded between 0 and pi for you to assert that S_n = arctan a.
    so do i just have to state that 0=<arctanx=<pi/2 ?
    also how do i even prove tanS(n)=n/(n+1) without using the tan formula to show that S(k)= arctann/(n+1) + arctan1/2k^2 ?
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    (Original post by Zacken)
    Well, no - tan S_n = a and S_n = arctan a are two different things, remember that tangent is a pi-periodic function, so how do you know that it's know S_n = arctan a + pi, for example? You need to prove that S_n is bounded between 0 and pi for you to assert that S_n = arctan a.
    ya mean -pi/2,pi/2
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    (Original post by porridgepie)
    so do i just have to state that 0=<arctanx=<pi/2 ?
    also how do i even prove tanS(n)=n/(n+1) without using the tan formula to show that S(k)= arctann/(n+1) + arctan1/2k^2 ?
    No, of course not. You have to prove it.

    Well, you do it by induction.
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    (Original post by Zacken)
    No, of course not. You have to prove it.

    Well, you do it by induction.
    sorry so do i start by showing tan(arctan.5 + arctan.125...+arctan1/2k^2) =n/(n+1) then do the k+1 induction
    i realise i must sound like a moron but i'm just really pants at induction proof
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    (Original post by porridgepie)
    sorry so do i start by showing tan(arctan.5 + arctan.125...+arctan1/2k^2) =n/(n+1) then do the k+1 induction
    i realise i must sound like a moron but i'm just really pants at induction proof
    yes
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    (Original post by porridgepie)
    sorry so do i start by showing tan(arctan.5 + arctan.125...+arctan1/2k^2) =n/(n+1) then do the k+1 induction
    i realise i must sound like a moron but i'm just really pants at induction proof
    No, you assume that tan (arctan 0.5 + ...) = n/n+1 and then use that assumption to prove that the k+1 case is also true.

    (Original post by porridgepie)
    the question tells you that arctan is in interval (0, pi/2)
    Exactly, hence why you need to prove that S_n is bounded above by pi/2 in order to apply the arctan function.
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    (Original post by Zacken)
    No, you assume that tan (arctan 0.5 + ...) = n/n+1 and then use that assumption to prove that the k+1 case is also true.



    Exactly, hence why you need to prove that S_n is bounded above by pi/2 in order to apply the arctan function.
    get it now thx for your help
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    (Original post by porridgepie)
    get it now thx for your help
    No worries.
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    So here is how I did:

    Started off with question 2 (because calculus is usually my best and it looked easy) and I completed it.

    Then I took up question 4 (more calculus ) did the first bit; used the first result in the second bit to give another differential equation and after squaring tried to find f(x) cant remember what I got but it was something weird not sure whether its right. Didnt give a geometric interpretation (or whatever was asked)

    Question 1 and 3 came next - 1 was good i proved all the results then got factors in (ii) which I think are correct. As for question three the graphs were fine i saw sin3<sin2 which was good and i showed open and coloured circles where needed and I hope I got it completely.

    Then I went for Q10 cuz it looked good but I couldnt complete it - i got the first result and then attempted (ii) after a lot of horrible algebra i came up with a weird cubic for lambda which i couldnt solve.

    The final question was the real mess - I had roughly 20-25 mins left and I just went for 11 but i couldnt get the first result - i did resolve and write down equations and stuff but the answer didnt come. I did write differentiate then equalise to zero to get maximum. I also did Q9 bc 11 wasnt going far but i think i made an error with reaction but i wrote down as many resolving equations and moments as was needed - that reaction error didnt give me the result i think.

    So how much do u guys think I would get? not really feeling very confident after messing up the last Q - looking back i think i shoulda done 8 instead of scratching at bits of mechanics questions at the end...
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    (Original post by Gunawardana)
    So here is how I did:

    Started off with question 2 (because calculus is usually my best and it looked easy) and I completed it.

    Then I took up question 4 (more calculus ) did the first bit; used the first result in the second bit to give another differential equation and after squaring tried to find f(x) cant remember what I got but it was something weird not sure whether its right. Didnt give a geometric interpretation (or whatever was asked)

    Question 1 and 3 came next - 1 was good i proved all the results then got factors in (ii) which I think are correct. As for question three the graphs were fine i saw sin3<sin2 which was good and i showed open and coloured circles where needed and I hope I got it completely.

    Then I went for Q10 cuz it looked good but I couldnt complete it - i got the first result and then attempted (ii) after a lot of horrible algebra i came up with a weird cubic for lambda which i couldnt solve.

    The final question was the real mess - I had roughly 20-25 mins left and I just went for 11 but i couldnt get the first result - i did resolve and write down equations and stuff but the answer didnt come. I did write differentiate then equalise to zero to get maximum. I also did Q9 bc 11 wasnt going far but i think i made an error with reaction but i wrote down as many resolving equations and moments as was needed - that reaction error didnt give me the result i think.

    So how much do u guys think I would get? not really feeling very confident after messing up the last Q - looking back i think i shoulda done 8 instead of scratching at bits of mechanics questions at the end...
    20, 16, 20, 15, 4, 8 = 86
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    (Original post by Zacken)
    20, 16, 20, 15, 4, 8 = 86
    I did 7 Qs btw (1,2,3,4,9,10,11) so wouldnt 1,2,3,4,10 and one of 9 or 11 be my best six? so wouldnt it be more like Q1=20, Q2=20, Q3=20? Q4=16, Q10=15, Q11=4? Q10=8? giving like more than 90?

    *Q9 = 8 not Q10 =8
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    (Original post by Gunawardana)
    I did 7 Qs btw (1,2,3,4,9,10,11) so wouldnt 1,2,3,4,10 and one of 9 or 11 be my best six? so wouldnt it be more like Q1=20, Q2=20, Q3=20? Q4=16, Q10=15, Q11=4? Q10=8? giving like more than 90?
    yeah, you put two questions in the same paragraph so I double counted.
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    (Original post by Zacken)
    yeah, you put two questions in the same paragraph so I double counted.
    yeah sry about that - and no worries. btw in my last post i meant Q10=15, Q11=4 and Q9(not 10) = 8 haha

    so yeah depends on where the S boundary would go - any guesses?
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    (Original post by Gunawardana)
    yeah sry about that - and no worries. btw in my last post i meant Q10=15, Q11=4 and Q9(not 10) = 8 haha

    so yeah depends on where the S boundary would go - any guesses?
    100+ i'd say
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    (Original post by Zacken)
    100+ i'd say
    thought so too - so yeah i guess ive gotten a good 1 (if all went as expected and i didnt make some ridiculously large error and didnt notice it )

    Well, good luck in STEP 2
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    (Original post by Gunawardana)
    thought so too - so yeah i guess ive gotten a good 1 (if all went as expected and i didnt make some ridiculously large error and didnt notice it )

    Well, good luck in STEP 2
    Yeah, reckon I got the same. Incredibly annoyed about that.

    Thanks, you too(?).
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    (Original post by Zacken)
    Yeah, reckon I got the same. Incredibly annoyed about that.

    Thanks, you too(?).
    np and thanks to u too - yeah im doing STEP 2 (and 3 as well)

    yeah annoyed about STEP 1 too, but I guess we shouldnt let that hold us back in STEP 2 and 3 haha . I just wanna make sure I choose my questions (mainly the last 1/2) well next time (cuz if i had selected a better last Q rather than scraping around i might have been able to get a better total) .
 
 
 
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