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Math Help - find the explicit formula for sequence

  1. #1
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    Unhappy find the explicit formula for sequence

    I'm having trouble with this problem, hopefully someone can help. I'm going crazy trying to figure this one out

    Find explicit ormulas for sequence of the form a1, a2, a3,... with the initial terms given.

    0, -1/2, 2/3, -3/4, 4/5, -5,65/7
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  2. #2
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    Quote Originally Posted by nikkie87 View Post
    damn i was typing to fast.
    0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7.
    First of all, notice that the denominator is always 1 more than the numerator (the first term is 0/1).

    So numerator = n, denominator = n + 1.

    Also notice that the terms have alternating sign.

    When n is odd, the terms are negative, when n is even, the terms are positive. What happens in the case of (-1)^n? The exact same thing. So we multiply each term by (-1)^n. This will alternate the signs.

    So each term is of the form...

    t_n = \frac{n}{n+1} (-1)^n, where n = 0,1,2 \dots
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