2007-11-27 14:14:29 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
f(n) = (-1)*n (n/(n+1)).
2007-11-27 14:18:13 · answer #1 · answered by Anonymous · 0⤊ 0⤋
(-1)^n * n/(n+1)
"an explicit formulas for this sequences"
correct formulation: an explicit formula for this sequence.
There is only one sequence, no need to use plural.
"0, -1/2, 2/3, -3/4"
Also you wrote only 4 terms, that is not a sequence.
Add dots to show that indeed is infinite:
0, -1/2, 2/3, -3/4, ...
2007-11-27 22:18:34 · answer #2 · answered by Theta40 7 · 0⤊ 0⤋
The first term of the sequence is 0, so f(1) = 0, giving f(n) = n - 1 so far. The denominator can be expressed as n, giving (n - 1) / n. The alternating sign is taken care of with (-1)^m. since even terms of the sequence are negative, use m = n - 1
The final formula, then becomes
f(n) = (n - 1)(-1)^(n - 1) / n
2007-11-27 22:39:41 · answer #3 · answered by Helmut 7 · 0⤊ 0⤋