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Math Help - show series is decreasing

  1. #1
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    show series is decreasing

    show \{ \frac{1}{2n + 1} \}_{n = 1}^{\infty} is strictly decreasing.
    for a series to be decreasing the next term must be smaller than the current term. a_n > a_{n +1}

    2n +1 < 2(n +1) + 1 (n^th term and n^th + 1)

    2n + 1 < 2n +3

    \frac{1}{2n +1} > \frac{1}{2n + 3}
    the next term is less than the previous therfor the series is decreasing.

    Am I correct?
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  2. #2
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    this sequence (not correct to call it a series, a series infers a summation) is decreasing.

    As n \rightarrow \infty , \frac{1}{2n+1} \rightarrow 0
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  3. #3
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    Quote Originally Posted by pickslides View Post
    this sequence (not correct to call it a series, a series infers a summation) is decreasing.

    As n \rightarrow \infty , \frac{1}{2n+1} \rightarrow 0
    I get it, sequence set/list of terms. I know it goes to zero just by looking at the n in the denominator and 1 in the numerator, but I have to show that it is decreasing. That is my question, did i show the sequences is decreasing, satisfactorily?
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  4. #4
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    Yeppers
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