(a)
Simplify 1 / [(√k) + √(k + 1)] , where k >= 0.
(b)
Hence find the value of the following.
{ 1 / [1+ (√2)] } + { 1 / [(√2) + (√3)] } + { 1 / [(√3) + (√4)] } + { 1 / [(√4) + (√5)] } + ... + { 1 / [(√8) + (√9)] }
F.4 maths---help...
2009-09-09 6:26 am
回答 (1)
2009-09-09 6:38 am
✔ 最佳答案
a) 1 / [(√k) + √(k + 1)] = [(√k) - √(k + 1)] / { [(√k) + √(k + 1)] [(√k) - √(k + 1)] }
= [(√k) - √(k + 1)] / [ k - (k+1)
= √(k + 1) - √k
b) { 1 / [1+ (√2)] } + { 1 / [(√2) + (√3)] } + { 1 / [(√3) + (√4)] } + { 1 / [(√4) + (√5)] } + ... + { 1 / [(√8) + (√9)] }
= (√2 - √1) + (√3 - √2) + (√4 - √3) + (√5 - √4)+...+ (√9 - √8)
= - √1 + √9
= - 1 + 3
= 2
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https://hk.answers.yahoo.com/question/index?qid=20090908000051KK01814