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    how to solve this? it is question 8
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    (Original post by Akhito Kanbara)
    how to solve this? it is question 8
    I have an idea, got the answer as 1. The trick is to notice the pattern and use some substitutions. Before I post my method, what have you tried though?
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    (Original post by Akhito Kanbara)
    how to solve this? it is question 8
    The trick to these sorts of questions is to realise its far to complicated to actually evaluate them.You need to use the fact that these expressions are truly infinite and thus you can rewrite them(effectively the same as applying certain functions to them) without changing them and thus use this to write an algebraic equation for those expressions for the top and bottom and divide the answers you find.
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    (Original post by Akhito Kanbara)
    how to solve this? it is question 8
    What happens if you cube the expression?
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    I tried them to see the pattern for geometric progression i dun think it has

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    This wat i reach use dalik way

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    (Original post by Akhito Kanbara)
    This wat i reach use dalik way

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    That doesn't lead you anywhere, or perhaps I don't follow.

    Try this:
    Let x=\sqrt[3]{4\sqrt[3]{4\sqrt[3]{4...}}}
    Then by definition x=\sqrt[3]{4x}

    Solve for x and disregard any solutions which do not fit this (such as 0).

    Then let y=\sqrt{2\sqrt{2\sqrt{2...}}} and apply the same trick and solve for y while disregarding any solutions which don't fit in.

    If you observe, you final answer should be \frac{x}{y}
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    Bah, I don't agree with questions like these, you need to prove that the sequence x_{n+1} = \sqrt{2 x_{n}} converges for you to make any reasonable use of the techniques above. Otherwise you can come up with some truly nonsensical results.
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    You could define a sequence say  x_{n+1} = \sqrt[3]{4x_n}, x_1 =1 . You should know how to find the limit of the sequence (given that it converges - no proof needed) as its basic C2.
    You can do a similar thing for the denominator. And the answer you need will be  \displaystyle \lim_{n\to\infty} \frac{x_n}{y_n} .
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    (Original post by Zacken)
    Bah, I don't agree with questions like these, you need to prove that the sequence x_{n+1} = \sqrt{2 x_{n}} converges for you to make any reasonable use of the techniques above. Otherwise you can come up with some truly nonsensical results.
    Yes, it will have people believe that  \text{u}_{n+1}=2\text{u}_n+1 is 1.
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    (Original post by B_9710)
    Yes, it will have people believe that  \text{u}_{n+1}=2\text{u}_n+1 is 1.
    Or that \displaystyle x^{x^{x}^{\cdots}} = 2 and  \displaystyle x^{x^{x}^{\cdots}} = 4 converges to the same x. Hitch is that only the first one is right since it only converges in [e^{-1}, e] or something similar.
 
 
 
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