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    Attachment 534435
    Stuck on part 3, I've tried and cant get to the final answer.
    Could someone show me the algebra please!
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    (Original post by Vanilla Poison)
    Attachment 534435
    Stuck on part 3, I've tried and cant get to the final answer.
    Could someone show me the algebra please!
    Show us what you already have.
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    (Original post by Zacken)
    Show us what you already have.
    I've got as far as 2/(2k-1)+2
    not sure where to go from there
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    (Original post by Vanilla Poison)
    I've got as far as 2/(2k-1)+2
    not sure where to go from there
    Your conjecture is that u_n = \frac{2}{2k-1}, yeah?

    So verify that works for u_1.

    Then show that \displaystyle u_{k+1} = \frac{\frac{2}{2k-1}}{1 + \frac{2}{2k-1}} = \frac{2}{2k-1 + 2} = \frac{2}{2(k+1) -1}

    and you're done... that's the same form of u_k except it has k+1 in place of k as we'd expect in an induction, so that's sorted.
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    (Original post by Zacken)
    Your conjecture is that u_n = \frac{2}{2k-1}, yeah?

    So verify that works for u_1.

    Then show that \displaystyle u_{k+1} = \frac{\frac{2}{2k-1}}{1 + \frac{2}{2k-1}} = \frac{2}{2k-1 + 2} = \frac{2}{2(k+1) -1}

    and you're done... that's the same form of u_k except it has k+1 in place of k as we'd expect in an induction, so that's sorted.
    Thanks Zacken! One thing I don't get is when you're showing n=k+1, why is Uk on top of the fraction. Is it because it says it in the question?
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    (Original post by Vanilla Poison)
    Thanks Zacken! One thing I don't get is when you're showing n=k+1, why is Uk on top of the fraction. Is it because it says it in the question?
    Yep. The question says that u_{k+1} = \frac{u_k}{1 + u_k} so that's the relation you use.
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    (Original post by Zacken)
    Yep. The question says that u_{k+1} = \frac{u_k}{1 + u_k} so that's the relation you use.
    You're a life saver!
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    (Original post by Vanilla Poison)
    You're a life saver!
    Thanks! :lol:
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    (Original post by Vanilla Poison)
    You're a life saver!
    Were you just self studying further maths because to do AS Further Maths in year 13, or just for fun, or were you doing Further Maths AS in year 12? XD


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    (Original post by Chittesh14)
    Were you just self studying further maths because to do AS Further Maths in year 13, or just for fun, or were you doing Further Maths AS in year 12? XD


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    Actually did further maths in year 12 Scraped an A somehow, I did M1 & M2 so the first year was slightly tricky.
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    (Original post by Vanilla Poison)
    Actually did further maths in year 12 Scraped an A somehow, I did M1 & M2 so the first year was slightly tricky.
    Taking the hard way out... Haha, no problem. The fact that you got an A doing FP1, M1 and M2 is enough man... Lol
    I can't believe I helped you on a question and now you destroying maths literally lol


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    (Original post by Chittesh14)
    Taking the hard way out... Haha, no problem. The fact that you got an A doing FP1, M1 and M2 is enough man... Lol
    I can't believe I helped you on a question and now you destroying maths literally lol


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    How about yourself, what subjects are you taking? I'm sure you can do the same with a little bit of effort
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    (Original post by Vanilla Poison)
    How about yourself, what subjects are you taking? I'm sure you can do the same with a little bit of effort
    Let's hope so. I don't even know to be honest, I'm the most unorganised guy in the world lol. I still have to buy suits, new bag, new everything lol. Even decide my new A-level options because my sixth form can't let me do my A-level options because the timetables clash...

    But, it's going to be either:

    Maths, further maths and economics
    Or maths, further maths, economics and physics but I self teach further maths so I can go to economics lessons.

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    (Original post by Chittesh14)
    Let's hope so. I don't even know to be honest, I'm the most unorganised guy in the world lol. I still have to buy suits, new bag, new everything lol. Even decide my new A-level options because my sixth form can't let me do my A-level options because the timetables clash...


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    That really sucks, perhaps you could self teach the subjects they wont let you choose. It's only the beginning of the year, you'll get into the hang of things and become more organised as time goes by!
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    (Original post by Vanilla Poison)
    That really sucks, perhaps you could self teach the subjects they wont let you choose. It's only the beginning of the year, you'll get into the hang of things and become more organised as time goes by!
    No, really I am unorganised since like 5 years lmao. Since I got lazy, I've gone unorganised. I think I'll change now I think...
    I might self teach further maths but let's see...
    Thanks thoug

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