T1 = 2
T2 = 6
T3 = 12
T4 = 20
Tn = ?
用Sn(等差總和)個條式~show埋steps
thx
急!!!!數學的等差數列之"三角形數列"
2010-04-22 7:36 pm
回答 (5)
2010-04-22 8:02 pm
✔ 最佳答案
T1 = 2
T2 = 6
T3 = 12
T4 = 20
Tn = ?
求Sn
Sol
T1=2*1
T2=3*2
T3=4*3
T4=5*4
…
Tn=(n+1)*n
Sn=T1+T2+T3+…+Tn
=sigma(k=1 to n)_Tk
=sigma(k=1 to n)_(k+1)*k
=sigma(k=1 to n)_k^2+sigmas(k=1 to n)_k
=n(n+1)(2n+1)/6+n(n+1)/2
=n(n+1)/6*[(2n+1)+3]
=n(n+1)/6*[2n+4]
=n(n+1)(n+2)/3
2010-04-22 14:01:26 補充：
Sn是n項和
Tn=(n+1)*n
代 n=2
T2=(2+1)*2=6
2010-04-23 3:40 am
T1 = 2
T2 = 2+4
T3 = 2+4+6
T4 = 2+4+6+8
Tn
= 2+4+6+8+....+(2n)
= 2(1+2+3+4+...+n)
= 2 [(1/2)(n)(n+1)]
= n(n+1)
T2 = 2+4
T3 = 2+4+6
T4 = 2+4+6+8
Tn
= 2+4+6+8+....+(2n)
= 2(1+2+3+4+...+n)
= 2 [(1/2)(n)(n+1)]
= n(n+1)
2010-04-22 7:58 pm
我上面寫左等差數列之 三角形數列
佢地之間ge野係 4 , 6 , 8
咁佢地個差ge差係 2
可以用到等差總和個條式黎求
明嗎?
佢地之間ge野係 4 , 6 , 8
咁佢地個差ge差係 2
可以用到等差總和個條式黎求
明嗎?
2010-04-22 7:49 pm
這個不是等差數列~~~~
2010-04-22 7:46 pm
a=2
d=T2-T1=6-2=4
Tn=a+d(n-1)=2+4(n-1)=2+4n-4=4n-2
d=T2-T1=6-2=4
Tn=a+d(n-1)=2+4(n-1)=2+4n-4=4n-2
收錄日期: 2021-04-13 17:12:15
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