根号2+1分之1+根号3+2分之1+根号4+3分之1+.+根号2007+2008分之1
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根号2+1分之1+根号3+2分之1+根号4+3分之1+.+根号2007+2008分之1
根号2+1分之1+根号3+2分之1+根号4+3分之1+.+根号2007+2008分之1
根号2+1分之1+根号3+2分之1+根号4+3分之1+.+根号2007+2008分之1
1/(√2+1)+1/(√3+√2)+1/(√4+√3)+.+1/(√2007+√2008)
=(√2-1)/(√2+1)(√2-1)+(√3-√2)/(√3+√2)(√3-√2)+(√4-√3)/(√4+√3)(√4-√3)+.+(√2008-√2007)/(√2007+√2008)(√2008-√2007)
=√2-1+√3-√2+√4-√3+.+√2008-√2007
=√2008-1
=2√502-1
所有式分母有理化
1/(√(n+1)+√n)=√(n+1)-√n
1/(√2+1)+1/(√3+√2)+1/(√4+√3)+...+1/(√2008+√2007)
=√2-√1+√3-√2+√4-√3+√5-√4+...+√2008-√2007
=√2008-1
1/(√2+1)+1/(√3+√2)+1/(√4+√3)+...............+1/(√2007+√2008)
=(√2-1)/(√2+1)(√2-1)+(√3-√2)/(√3+√2)(√3-√2)+(√4-√3)/(√4+√3)(√4-√3)+...............+(√2008-√2007)/(√2007+√2008)(√2008-√2007)
=√2-1+√...
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1/(√2+1)+1/(√3+√2)+1/(√4+√3)+...............+1/(√2007+√2008)
=(√2-1)/(√2+1)(√2-1)+(√3-√2)/(√3+√2)(√3-√2)+(√4-√3)/(√4+√3)(√4-√3)+...............+(√2008-√2007)/(√2007+√2008)(√2008-√2007)
=√2-1+√3-√2+√4-√3+...............+√2008-√2007
=√2008-1
=2√502-1
我算的结果也是这样。。
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