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Math Help - simplify: (x+1/x) + (x^2 + 1/x^2)^2 +...+(x^n + 1/x^n)^n

  1. #1
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    simplify: (x+1/x) + (x^2 + 1/x^2)^2 +...+(x^n + 1/x^n)^n

    I would love to show ANY effort of my own, but it seams to me that I should use some theorem (of which I have never heard of) in order to attack this problem.

    Help, please!
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  2. #2
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    Re: simplify: (x+1/x) + (x^2 + 1/x^2)^2 +...+(x^n + 1/x^n)^n

    hello there notice that u can seperate this sequence
    into two sequences which are both geometric
    the first is:x+x^2+x^3+...........+x^n
    the second is:1/x +1/x^2+1/x^3+.........1/x^n
    now just use the formula for the sum of ageometric sequence
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  3. #3
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    Re: simplify: (x+1/x) + (x^2 + 1/x^2)^2 +...+(x^n + 1/x^n)^n

    Quote Originally Posted by islam View Post
    hello there notice that u can seperate this sequence into two sequences which are both geometric
    the first is:x+x^2+x^3+...........+x^n
    the second is:1/x +1/x^2+1/x^3+.........1/x^n
    now just use the formula for the sum of ageometric sequence
    That is not the case.
    For example: \left( {x^3  + \frac{1}{{x^3 }}} \right)^3  = x^9  + 3x^3  + 3x^{ - 3}  + x^{ - 9}
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  4. #4
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    Re: simplify: (x+1/x) + (x^2 + 1/x^2)^2 +...+(x^n + 1/x^n)^n

    sorry very sorry
    i just missed the exponent
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  5. #5
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    Re: simplify: (x+1/x) + (x^2 + 1/x^2)^2 +...+(x^n + 1/x^n)^n

    I'm starting to think the whole problem was a typo, and the real form should be:
    (x+1/x) + (x^2 + 1/x^2) +...+(x^n + 1/x^n)
    so it's quite simple.

    But thanks for the help!
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  6. #6
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    Re: simplify: (x+1/x) + (x^2 + 1/x^2)^2 +...+(x^n + 1/x^n)^n

    Quote Originally Posted by witek123 View Post
    I'm starting to think the whole problem was a typo, and the real form should be:
    (x+1/x) + (x^2 + 1/x^2) +...+(x^n + 1/x^n)
    so it's quite simple.
    I agree with that.
    If that is the case reply #2 answers that question.
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