The general term of a sequence is given as T(n) = (sqrt 2)^(n - 1). Find the value of :
T(1) x T(3) x T(5) x T(7) x ...........x T(2n - 1) in terms of n.
Sequence
2012-12-07 3:58 pm
回答 (1)
2012-12-07 4:16 pm
✔ 最佳答案
Answer : (sqrt 2)^[n(n - 1)]Solution:
T(1) x T(3) x T(5) x T(7) x ...........x T(2n - 1)
= (sqrt 2)^(0) x (sqrt 2)^(2) x (sqrt 2)^(4) x (sqrt 2)^(6) + ... + (sqrt 2)^(2n - 2)
= (sqrt 2)^[0 + 2 + 4 + 6 + ... (2n - 2)]
= (sqrt 2)^{(n / 2)[2(0) + (n - 1)(2)]}
= (sqrt 2)^[n(n - 1)]
參考: knowledge
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https://hk.answers.yahoo.com/question/index?qid=20121207000051KK00048