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    hi, so i'd really appreciate it if someone could take the time to look at this textbook example and explain how the textbook got from the the second last line to the final answer for bii:

    http://24.media.tumblr.com/933491ad5...0nxo1_1280.jpg

    i think it's just the indices part that i'm having trouble with.
    if someone could maybe break it down into smaller steps then that'd be amazing.
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    (Original post by PurpleSquid)
    hi, so i'd really appreciate it if someone could take the time to look at this textbook example and explain how the textbook got from the the second last line to the final answer for bii:

    http://24.media.tumblr.com/933491ad5...0nxo1_1280.jpg

    i think it's just the indices part that i'm having trouble with.
    if someone could maybe break it down into smaller steps then that'd be amazing.
    Remember that (\frac{1}{2})^{n-1} = \frac{1}{2^{n-1}}

    and then just break up what you've got into:

    5 \ctimes (-1)^{n-1} \ctimes \frac{2^3}{2^{n-1}}

    In your final fraction divide top and bottom by 2^3 and you get what they've got
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    (Original post by PurpleSquid)
    hi, so i'd really appreciate it if someone could take the time to look at this textbook example and explain how the textbook got from the the second last line to the final answer for bii:

    http://24.media.tumblr.com/933491ad5...0nxo1_1280.jpg

    i think it's just the indices part that i'm having trouble with.
    if someone could maybe break it down into smaller steps then that'd be amazing.
    So:
    You split up the brackets:
    Spoiler:
    Show
    (-\frac{1}{2})^{n-1} = (-1)^{n-1} \times (\frac{1}{2})^{n-1}

    Then you have:
    Spoiler:
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    (-1)^{n-1} \times (\frac{1}{2})^{n-1} \times 5 \times 2^3
    Now note that \ 8 = (\frac{1}{2})^{-3}

    Now:
    Spoiler:
    Show
    (-1)^{n-1} \times 5 \times (\frac{1}{2})^{n-1} \times (\frac{1}{2})^{-3}


    Recombine everything using laws of indices:
    Spoiler:
    Show
    (-1)^{n-1} \times 5 \times (\frac{1}{2})^{n-4}

    Now rewrite as:
    Spoiler:
    Show
    (-1)^{n-1}\times (\frac{5}{2})^{n-4}
    • Thread Starter
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    (Original post by davros)
    Remember that (\frac{1}{2})^{n-1} = \frac{1}{2^{n-1}}

    and then just break up what you've got into:

    5 \ctimes (-1)^{n-1} \ctimes \frac{2^3}{2^{n-1}}

    In your final fraction divide top and bottom by 2^3 and you get what they've got
    thanks!

    EDIT: thank you both!
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    (Original post by PurpleSquid)
    thanks!

    EDIT: thank you both!
    Any time
 
 
 
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