1/(1+√2)+1/(√2+√3)+1/(√3+√4)+.1/(√2012+√2013)

来源:学生作业帮助网 编辑:作业帮 时间:2024/03/29 04:25:38
1/(1+√2)+1/(√2+√3)+1/(√3+√4)+.1/(√2012+√2013)

1/(1+√2)+1/(√2+√3)+1/(√3+√4)+.1/(√2012+√2013)
1/(1+√2)+1/(√2+√3)+1/(√3+√4)+.1/(√2012+√2013)

1/(1+√2)+1/(√2+√3)+1/(√3+√4)+.1/(√2012+√2013)
1/(1+√2)+1/(√2+√3)+1/(√3+√4)+.1/(√2012+√2013)
=(√2-1)/(1+√2)(√2-1) + (√3-√2)/(√3+√2)(√3-√2) +(√4-√3)/(√4+√3)(√4-√3)+……+
(√2013-√2012)/(√2013+√2012)(√2013-√2012)
= √2-1 + √3 -√2 + √4 -√3 + …… + √2013 -√2012
= √2013 - 1