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    2/3 , 6/7 , 14/15 , 30/31

    i split it from top and bottom:
    2, 6, 14, 30...
    3, 7, 15, 31...

    I can't seem to do much with this, im guessing its 4^n then somthing,
    as the 'common' difference is 4, (i use ' ' seeing as its not really common, im sure you know what i mean), but i cant really see what to do now, is there some method/formula to work something like this out?
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    Well, looking at the bottom first, an obvious pattern jumps out (related to 4^n)
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    Not sure 4^n is really the thing to be looking at...
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    Top: U_{n+1}=2(U_n +1)
    Bottom: U_{n+1} = 2U_n + 1


    I know it's not really the nth term, but it's a start. :P
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    It looks like n+(n+1)+1/n+(n+1)+2

    ie, 2+3+1 = 6
    2+3+2 = 7

    6+7+1 = 14
    6+7+2 = 15 etc etc
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    Think I got it.

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     U_n = \frac{2^{n+1}-2}{2^{n+1}-1}
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    (Original post by Pork and Beans)
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    Top: U_{n+1}=2(U_n +1)
    Bottom: U_{n+1} = 2U_n + 1


    I know it's not really the nth term, but it's a start. :P
    yh, i saw that, but i dont know how you'd work out an nth term formula from that
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    (Original post by Pork and Beans)
    Think I got it.

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     U_n = \frac{2^{n+1}-2}{2^{n+1}-1}
    that does seem to work, how did u get that? how come its 2^ , rather than 4^
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    ok yep thanks i get it now, your adding 2^n+1 every time, thanks
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    The difference in terms is being multiplied by 2 with each successive term, this is your clue that you need to be thinking in powers of two.
 
 
 
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