The sum of the first n terms of a sequence is Sn = 1/2 n ( n + 1 ). Find the nth term.
F5 Maths sequence
2011-11-05 6:00 am
回答 (3)
2011-11-05 6:16 am
✔ 最佳答案
您好，我是 lop，高興能解答您的問題。This is a famous formula :
1 + 2 + 3 + 4 + ... + ( n - 1 ) + n = n(n+1)/2
So , the nth term is n .
T(n) = n
參考: Hope I Can Help You ^_^ ( From me )
2011-11-05 6:52 am
the n th term
= S(n) - S(n - 1)
= (1/2)n(n + 1) - (1/2)(n - 1)n
= (1/2)(n)(n + 1 - n + 1)
= n
= S(n) - S(n - 1)
= (1/2)n(n + 1) - (1/2)(n - 1)n
= (1/2)(n)(n + 1 - n + 1)
= n
2011-11-05 6:19 am
n.
let the nth term be an+b.
1a+b+2a+b+3a+b+...+an+b=1/2n(n+1)
a(1+2+3+...+n)+b=1/2n(n+1)
1/2n(n+1)a+b=1/2n(n+1)
0.5an^2+0.5an+b=0.5n^2+0.5n
By comparing like terms, a=1,b=0
let the nth term be an+b.
1a+b+2a+b+3a+b+...+an+b=1/2n(n+1)
a(1+2+3+...+n)+b=1/2n(n+1)
1/2n(n+1)a+b=1/2n(n+1)
0.5an^2+0.5an+b=0.5n^2+0.5n
By comparing like terms, a=1,b=0
收錄日期: 2021-04-26 14:56:26
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20111104000051KK00773