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230问答网 > 化简:1⼀(1+√2)+1⼀(√2+√3)+1⼀(√3+√4)+1⼀(√4+√5)+1⼀(√5+√6)+1⼀(√6+√7)1⼀(√7+√8)+1⼀(√8+√9)

化简:1⼀(1+√2)+1⼀(√2+√3)+1⼀(√3+√4)+1⼀(√4+√5)+1⼀(√5+√6)+1⼀(√6+√7)1⼀(√7+√8)+1⼀(√8+√9)

2025-04-02 10:14:41

推荐回答（2个）

回答1：

1-√2/(1-√2)(1+√2)+ (√2-√3)/(√2-√3)(√2+√3)+....+(√8-√9)/(√8+√9)(√8-√9)
=-(1-√2)- (√2-√3)-(√3-√4)-....-(√8-√9)
=-1+√9
=2

回答2：

∵1／[√n＋√﹙n＋1﹚]=[√﹙n＋1﹚＋√n][√﹙n＋1﹚-√n]／[√n＋√﹙n＋1﹚]＝√﹙n＋1﹚－√n
∴√2－1＋√3－√2＋。。。＋√9－√8＝√9－1＝2

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