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Math Help - sequence converge, finding its limit.

  1. #1
    jax
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    sequence converge, finding its limit.

    Hello,
    I was wondering if this sequence converges, and if it does what is the limit?

    (a_n), where a_n=(1)+(1/2)+(1/2^2)+(1/2^3)+...+(1/2^n).

    p.s- I know that the sequence a_n=(1/2,1/4,1/6...) its limit is zero, but I'm not really sure about the sequence above.

    Thanks!!
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  2. #2
    MHF Contributor
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    Quote Originally Posted by jax View Post
    Hello,
    I was wondering if this sequence converges, and if it does what is the limit?

    (a_n), where a_n=(1)+(1/2)+(1/2^2)+(1/2^3)+...+(1/2^n).

    p.s- I know that the sequence a_n=(1/2,1/4,1/6...) its limit is zero, but I'm not really sure about the sequence above.

    Thanks!!
    I guess you mean "series", the sum of the terms of the sequence,
    and you want to know if this sum converges as n goes to infinity.

    So your a_n should be S_n

    This is a geometric series, 1st term 1 and common ratio 0.5

    Hence it's sum for n terms is \displaystyle\frac{1-r^n}{1-r}

    and as n goes to infinity, the numerator goes to 1, while the denominator is 0.5.

    So the sum converges.
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  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
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    Hint: Find formula for a_n... (geometric series).
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