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Math Help - cant seem to figure this series problem out.

  1. #1
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    cant seem to figure this series problem out.

    Let a_n be the n th digit after the decimal point in 4pi+4e.

    Evaluate ∑ a_n(.1)^n.
    n=1

    thanks for any help.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Ok

    Quote Originally Posted by waite3 View Post
    Let a_n be the n th digit after the decimal point in 4pi+4e.

    Evaluate ∑ a_n(.1)^n.
    n=1

    thanks for any help.
    This is a last ditch effort...this just an approximation but since if you actually looked at it the arithmetic mean of all the digits would be 5...therefore \sum_{n=0}^{\infty}a_{n}\bigg(\frac{1}{10}\bigg)^{  n}\approx{5}\cdot\frac{1}{1-\frac{1}{10}}
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  3. #3
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    can anyone do this problem?

    I've tried it along with many other people and so far no one has been able to get it. if any one can do this it would be nice . thanks for any help
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by waite3 View Post
    Let a_n be the n th digit after the decimal point in 4pi+4e.

    Evaluate ∑ a_n(.1)^n.
    n=1

    thanks for any help.
    Since a_n represents the nth digit of the decimal part of 4\pi + 4e wouldn't it be reasonable to say that
    \sum_{n = 1}^{\infty} a_n(0.1)^n = (4\pi - 4e) - \lfloor 4\pi + 4e \rfloor
    in other words the decimal part of 4\pi + 4e.

    As the two numbers are transcendental I would be very surprised to find that there is an exact answer other than this.

    -Dan
    l
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