What is the common different of (1-1/3+1/5 -1/7+1/9 -1/11....)?
2006-11-28 06:16:25 · 2 個解答 · 發問者 goodaskmansir 1 in 科學 ➔ 數學
let (-1)^(n-1)*(1/n) be the nth term of the sequence
the common different would be
(-1)^(n-1)*(1/n) - (-1)^(n)*(1/(n+1))
=(-1)^(n-1)*(1/n + 1/(n+1))
2006-11-28 07:39:15 · answer #1 · answered by chau 2 · 0⤊ 0⤋
Let nth term be (-1)^(n+1)．(1/(2n-1))
therefore the common different is
T(n+1)-T(n) = (-1)^(n+2)．(1/(2n+1)) + (-1)^(n+1)．(1/(2n-1)
=(-1)^(n+1)[ 1/(2n-1) - 1/(2n+1))
=(-1)^(n+1)[2/(4n^2-1)]
2006-11-28 08:05:21 · answer #2 · answered by HaHa 7 · 0⤊ 0⤋