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

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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- Sep 26th 2008, 03:24 PMnikkie87find 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 (Headbang)

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 - Sep 26th 2008, 04:24 PMProve It
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 $\displaystyle (-1)^n$? The exact same thing. So we multiply each term by $\displaystyle (-1)^n$. This will alternate the signs.

So each term is of the form...

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