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Geometric sequences question

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    Can someone please help me solve and explain how did you solve the question below? I am helping my friend and it looks like c2/fp1 stuff but I don't remember doing that with x's and not actual numbers, so is that perhaps c3 or something else? Thanks for explanations.
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    Someone please? I really need this as soon as possible.
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    Ignore 1/x for the minute and deal with x+x^2+.... How can you rewrite this? If you can, then you will get a simplified left hand side which can be rearranged and I think will be a quadratic to solve.
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    (Original post by WarriorInAWig)
    Ignore 1/x for the minute and deal with x+x^2+.... How can you rewrite this? If you can, then you will get a simplified left hand side which can be rearranged and I think will be a quadratic to solve.
    I'm sorry I didn't understand what you mean, nor did my friend. How can you ignore 1/x if its first term in the sequence? I tried using a/1-r formula but I would get something like 1/x - 1/x^2 = 3.5 but couldn't solve further, because even if its sort of like quadratic, powers are negative.
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    1/x + x + x^2 + x^3 +....= 3.5
    1/x + x (1 + x + x^2 + x^3 + ...) = 3.5
    1/x + x (1/(1-x)) = 3.5
    1/x + x/(1-x) = 3.5

    I hope that makes more sense.
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    As it stands you do not have a sequence because there is no common ratio

    If you ignore the 1/x (as was suggested) then you have a geometric sequence

    If you do not want to ignore it then +1 to both sides


    You now have 1/x + 1 + x + x^2 + .... = 4.5

    This is a geometric sequence and you can use the sum to infinity rule

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