0 2 5 9 14 20
+2 +3 +4 +5 +6
what is the n term?
find out 0,2,5,9 ' s n term
2008-12-12 6:21 am
回答 (3)
2008-12-12 8:29 am
✔ 最佳答案
T(1) = 0
T(2) = 0 + 2
T(3) = 0 + 2 + 3
T(4) = 0 + 2 + 3 + 4
T(5) = 0 + 2 + 3 + 4 + 5
T(6) = 0 + 2 + 3 + 4 + 5 + 6
Hence, the nth term, T(n)
= 0 + 2 + 3 + ...... + n
= (1 + 2 + 3 + ...... + n) - 1
= n(n + 1)/2 - 1
= (n2 + n)/2 - 1
= (n2 + n - 2)/2
= (n - 1)(n + 2)/2
2008-12-12 8:30 am
T(1) = 0 = -1 + [1]
T(2) = 2 = -1 + [1+2]
T(3) = 5 = -1 + [1+2+3]
T(4) = 9 = -1 + [1+2+3+4]
T(5) = 14 = -1 + [1+2+3+4+5]
T(6) = 20 = -1 + [1+2+3+4+5+6]
...
T(n) = -1 + [1+2+3+...+n]
Since 1+2+3+...+n = n(n+1)/2
Therefore
T(n) = -1 + n(n+1)/2 = [n^2 + n - 2] / 2
T(2) = 2 = -1 + [1+2]
T(3) = 5 = -1 + [1+2+3]
T(4) = 9 = -1 + [1+2+3+4]
T(5) = 14 = -1 + [1+2+3+4+5]
T(6) = 20 = -1 + [1+2+3+4+5+6]
...
T(n) = -1 + [1+2+3+...+n]
Since 1+2+3+...+n = n(n+1)/2
Therefore
T(n) = -1 + n(n+1)/2 = [n^2 + n - 2] / 2
參考: ME
2008-12-12 6:47 am
T1 = 0
T2 = 2 .... difference of T1 & T2 is 2
T3 = 5 .... difference of T2 & T3 is 3
T4 = 9 .... difference of T3 & T4 is 4
T5 = 14... difference of T4 & T5 is 5
T6 = 20... difference of T5 & T6 is 6
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Tn = x ... difference of T(n-1) & Tn is n
so
Tn = T(n-1) + n
T2 = 2 .... difference of T1 & T2 is 2
T3 = 5 .... difference of T2 & T3 is 3
T4 = 9 .... difference of T3 & T4 is 4
T5 = 14... difference of T4 & T5 is 5
T6 = 20... difference of T5 & T6 is 6
．
．
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Tn = x ... difference of T(n-1) & Tn is n
so
Tn = T(n-1) + n
參考: me
收錄日期: 2021-04-25 14:30:38
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