(1/((根号2)+1))+1/(根号3+根号2)+1/(根号4+根号3)+……+1/(根号2010+根号2009))×(根号2010+1)的值

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(1/((根号2)+1))+1/(根号3+根号2)+1/(根号4+根号3)+……+1/(根号2010+根号2009))×(根号2010+1)的值
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(1/((根号2)+1))+1/(根号3+根号2)+1/(根号4+根号3)+……+1/(根号2010+根号2009))×(根号2010+1)的值
(1/((根号2)+1))+1/(根号3+根号2)+1/(根号4+根号3)+……+1/(根号2010+根号2009))×(根号2010+1)的值

(1/((根号2)+1))+1/(根号3+根号2)+1/(根号4+根号3)+……+1/(根号2010+根号2009))×(根号2010+1)的值
1/(√2+1)+1/(√3+√2)+...+1/(√2010+√2009)(√2010+1)
=(√2-1+√3-√2+...+√2010-√2009)(√2010+1)
=(√2010-1)(√2010+1)
=2009

2009