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    Hey I'm only in my 4th week of uni and I'm struggling with a couple of my calculus questions. I've posted my attempts at all the questions, but am unsure where to go from there. Could some one please help me on them please ? The questions are 8b and 9 a and b Thank you
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    (Original post by Roxanne18)
    Hey I'm only in my 4th week of uni and I'm struggling with a couple of my calculus questions. I've posted my attempts at all the questions, but am unsure where to go from there. Could some one please help me on them please ? The questions are 8b and 9 a and b Thank you

    For 8b.

    You've shown it's true for S_2, and looks like you've going for induction.

    For your induction step, it's not clear whether you know what you're summing as you've put nothing under the summation signs, and what you have put doesn't look right.

    I suggest writing out S_{N+1} and S_N, subtract the latter from the former and see what you get. You should have three terms left.
    Hint: You want to show it's >0.
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    (Original post by ghostwalker)
    For 8b.

    You've shown it's true for S_2, and looks like you've going for induction.

    For your induction step, it's not clear whether you know what you're summing as you've put nothing under the summation signs, and what you have put doesn't look right.

    I suggest writing out S_{N+1} and S_N, subtract the latter from the former and see what you get. You should have three terms left.
    Hint: You want to show it's >0.
    Okay thank you, I will have a try at doing this now. I have just realised that I don't have to do it by induction, so would you think an approach like this would be better ? Is it a valid proof ?
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    (Original post by Roxanne18)
    Okay thank you, I will have a try at doing this now. I have just realised that I don't have to do it by induction, so would you think an approach like this would be better ? Is it a valid proof ?
    No.

    \displaystyle \sum_{l=1}^2\frac{1}{N+l}\not=  \frac{14}{24}

    Edit: That sum would actually depend on what the value of N is, and is only equal for N=2.


    I really do recommend writing out S_N and S_{N+1}, first and last few terms of each, so you can be clear what you're summing.
 
 
 
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