set positive numbers 1,t,1/2...be geometric sequence.
find product T(1)x T(3)x T(5)x...xT(2n-1)
answer,please use n to express
one maths question
2014-08-28 12:41 am
回答 (2)
2014-08-28 10:14 am
✔ 最佳答案
The answer is as follows :圖片參考：https://s.yimg.com/lo/api/res/1.2/gCqSRXhv.6E_nNhIb_ex_Q--/YXBwaWQ9dHdhbnN3ZXJzO3E9ODU-/https://farm4.staticflickr.com/3845/15055633275_ea8958454a_o.png
https://farm4.staticflickr.com/3845/15055633275_ea8958454a_o.png
參考: pingshek
2014-08-28 2:45 am
1 x (1/2) x (1/2)^2 x ... x (1/2)^(n-1)
=1/ [ 2 x 2^2 x 2^3 x ... x 2^(n-1) ]
=1/ [ 2^(1+2+3+...+n-1) ]
=1/ 2^[n(n-1)/2]
=2^[-n(n-1)/2]
=1/ [ 2 x 2^2 x 2^3 x ... x 2^(n-1) ]
=1/ [ 2^(1+2+3+...+n-1) ]
=1/ 2^[n(n-1)/2]
=2^[-n(n-1)/2]
收錄日期: 2021-04-30 17:19:20
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20140827000051KK00107