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Math Help - Subsequence

  1. #1
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    Subsequence

    Is {1, 3, 6, 10, 15, ...} a subsequence of the natural numbers and, if so, what function composed with the natural numbers gives this subsequence? Thanks.
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  2. #2
    MHF Contributor chisigma's Avatar
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    The difference equation that produces the subsequence is...

    \Delta_{n}= a_{n+1} - a_{n}= 1+n , a_{1}=1 (1)

    Kind regards

    \chi \sigma
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  3. #3
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    I am not sure how to make this work with what I have. I have the composition of f and g = [n(n+1)]/2 = {1, 3, 6, 10, 15, ...}. I know that f = {1, 2, 3, 4, ...}. I need to find g.
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  4. #4
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    Let f(1)=1, f(2)=3, f(3)=6, f(4)=10, f(5)=15 and so on. Then

    f(1)=1
    f(2)-f(1)=2
    f(3)-f(2)=3
    f(4)-f(2)=4
    ...............
    f(n)-f(n-1)=n

    Adding these f(n)=n(n+1)/2
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