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Thread: Finding the general formula of a given sequence:

  1. #1
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    Unhappy Finding the general formula of a given sequence:

    Hi guys! I'm doing a homework problem asking to find the general formula of a sequence of numbers and I'm having a really tough time trying to figure out the numerator. The sequence is as follows where n=1 : (8/(12+1)) , (1/(22+ 1)), (8/(32 + 1)), (1/(42 + 1)) ...<br><br>I understand the numerator is just n2+ 1 but how do I make numbers alternate like that? I've been at it for a while and I just cant seem to get it.<br><br>Thanks for the help!
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  2. #2
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    Re: Finding the general formula of a given sequence:

    $n_k = \dfrac 7 2 \left((-1)^{k-1}+1\right) + 1 = \{8,1,8,1, \dots\}$

    $d_k = \dfrac{1}{n^2+1}$

    $s_k = \dfrac{n_k}{d_k}$
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  3. #3
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    Re: Finding the general formula of a given sequence:

    omg thanks so much! now I can utilize this for situations involving alternating numbers like that
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  4. #4
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    Re: Finding the general formula of a given sequence:

    There are other methods but (COS(n*π)+1) and 1-((-1^n + 1) / 2) will both osculate between 0 and 1
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