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    Just wondering if this is the correct method for answering the question at the top of the page, undoubtedly there's a few mistakes, so could somebody point me in the right direction please!

    Thanks a lot, klaxoii


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    (Original post by Klaxoii)
    Just wondering if this is the correct method for answering the question at the top of the page, undoubtedly there's a few mistakes, so could somebody point me in the right direction please!

    Thanks a lot, klaxoii


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    The (k+1)th term is not

    \dfrac{k+1}{k+2}

    You need to show that the sum to k+1 is that.

    Hint:

    The r(th) term is given by.

    \dfrac{1}{r(r+1)}


    Sum to k+1 = sum to k + (k+1)th term.
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    (Original post by Klaxoii)
    Just wondering if this is the correct method for answering the question at the top of the page, undoubtedly there's a few mistakes, so could somebody point me in the right direction please!

    Thanks a lot, klaxoii


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    Some small details have been missed which would mean you lose marks, eg at the start sub in 1 into LHS and RHS, also its helpful to sub k+1 into original summation formula so you know what you are aiming for. Conclusion at the end isn't finished. Here's a different question I did, that's how I think it should be set out for guaranteed full marks, sorry about the bad handwriting

    EDIT: I see you subbed k+1 into the original summation formula but you have to show that sum of r= 1 to k+1th term is equal to this. As mentioned above sum up to k + (k+1)th term is required
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    (Original post by Klaxoii)
    Just wondering if this is the correct method for answering the question at the top of the page, undoubtedly there's a few mistakes, so could somebody point me in the right direction please!

    Thanks a lot, klaxoii


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    You've made quite a few mistakes and Indeterminate has given the main one but here's a few tips.

    Firstly, after 'when n=1' you have written an equation which is true for n=1 but you haven't really shown that both sides of the original equation are 1/2 with a substitution of n=1.

    Try to be thorough e.g. you could say, When n=1:

    \displaystyle \sum_{r=1}^n \frac{1}{r(r+1)} = ...

    and \displaystyle \frac{n}{n+1} = ...


    Also, after you've written 'assume true for n=k', you've written an expression that doesn't really mean anything. You must make sure that all your working is readable.
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    (Original post by raiden95)
    Some small details have been missed which would mean you lose marks, eg at the start sub in 1 into LHS and RHS, also its helpful to sub k+1 into original summation formula so you know what you are aiming for. Conclusion at the end isn't finished. Here's a different question I did, that's how I think it should be set out for guaranteed full marks, sorry about the bad handwriting
    Thanks a lot, to both, i'll put into practise what you've said!


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    (Original post by raiden95)
    Some small details have been missed which would mean you lose marks, eg at the start sub in 1 into LHS and RHS, also its helpful to sub k+1 into original summation formula so you know what you are aiming for. Conclusion at the end isn't finished. Here's a different question I did, that's how I think it should be set out for guaranteed full marks, sorry about the bad handwriting
    Someone forgot to check the sticky page
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    (Original post by Klaxoii)
    Thanks a lot, to both, i'll put into practise what you've said!


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    Also, your conclusion should be something like:

    "From the assumption that the result is true for n=k, we get that it is also true for n=k+1. Therefore, as it is true for n=1, it is true for all n \geq 1 (where n is an integer) by mathematical induction".
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    (Original post by lebron_23)
    Someone forgot to check the sticky page
    Its a different question i sent though, so i guess its allowed
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    (Original post by raiden95)
    Its a different question i sent though, so i guess its allowed
    Dammit I didn't check, I just wanted to grill you :cool:

    Aside from that, how's revision going? Evidently you're cool with FP1 lol..
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    In addition to what's said above, my teacher said to label what you are assuming to be true (the bit where you put k in) the 'induction hypothesis'. Then when you use it later, say that this is by the induction hypothesis.
    As said before, it might be helpful to clearly state what you are trying to prove so the examiner knows and you know what you're trying to find.



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    (Original post by lebron_23)
    Dammit I didn't check, I just wanted to grill you :cool:

    Aside from that, how's revision going? Evidently you're cool with FP1 lol..
    Yeah fp1 isn't bad I try do do at least about 40mins a day of it, should be good. Might do the last parts of induction you?
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    (Original post by raiden95)
    Yeah fp1 isn't bad I try do do at least about 40mins a day of it, should be good. Might do the last parts of induction you?
    Haven't done much on it if I'm honest, but the exam is quite late and there's not much content so I guess most of my FP1 revision will happen in the half term of may. Other than that, I'm basically about to finish D1, finished S1 a little while back and the rest is cool. Who knows, I may even have a look at my chemistry book soon :rolleyes:
 
 
 
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