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    How would I go about proving that if the sum from n=k to infinity of 1/n(n+1) is 1/k, then the sum from n=k to infinity of 1/(n+1)^2 < 1/k?
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    (Original post by Kolasinac138)
    How would I go about proving that if the sum from n=k to infinity of 1/n(n+1) is 1/k, then the sum from n=k to infinity of 1/(n+1)^2 < 1/k?
    Look at each term of the first series and then look at each term in the second series. What do you notice and how can you use that to help with your proof?
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    (Original post by Slowbro93)
    Look at each term of the first series and then look at each term in the second series. What do you notice and how can you use that to help with your proof?
    Ok, so first series =

    1/2, 1/6, 1/12

    2nd series =

    1/4, 1/9, 1/16

    Not sure ..
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    (Original post by Kolasinac138)
    Ok, so first series =

    1/2, 1/6, 1/12

    2nd series =

    1/4, 1/9, 1/16

    Not sure ..
    Well notice that the terms within the second one are smaller then the first one. So what will happen when you add them together givne that you're told the first set of terms add up to \frac{1}{k}?
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    (Original post by Kolasinac138)
    How would I go about proving that if the sum from n=k to infinity of 1/n(n+1) is 1/k, then the sum from n=k to infinity of 1/(n+1)^2 < 1/k?
    Heres the solution. You have to prove it algebraically.Name:  IMG_20150511_141223.jpg
Views: 95
Size:  501.0 KBI hope the image is clear.
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    (Original post by tahmiin)
    Heres the solution. You have to prove it algebraically.I hope the image is clear.
    Please don't post full solutions to problems - it's against forum rules

    (In this case you've actually gone into far too much detail - you can compare the sizes of terms in the two series much more easily!)
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    (Original post by davros)
    Please don't post full solutions to problems - it's against forum rules

    (In this case you've actually gone into far too much detail - you can compare the sizes of terms in the two series much more easily!)
    Ooo, sorry I had no idea. I'm new to TSR. And yeah I spotted it straight away but I wanted to properly explain it.. which i guess i should not be doing.. Can I ask why I cant post full solutions??
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    (Original post by tahmiin)
    . Can I ask why I cant post full solutions??
    Basically we try to stick to providing hints and guidance so that students can work things out for themselves with a bit of advice.

    See the official guide to posting for further info:

    http://www.thestudentroom.co.uk/showthread.php?t=403989
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    (Original post by davros)
    Basically we try to stick to providing hints and guidance so that students can work things out for themselves with a bit of advice.

    See the official guide to posting for further info:

    http://www.thestudentroom.co.uk/showthread.php?t=403989
    I understand, thanks!
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    Thanks, I pretty much got that method but felt it is somewhat hand-wavy.
 
 
 
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