(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

来源:学生作业学帮网 编辑:学帮网 时间:2024/06/28 16:56:46

(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