find the explicit formula for sequence

Quote:

Originally Posted by nikkie87

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 $n = 0,1,2 \dots$