试求1除以根号2加1加1除以根号3加根号2加...加1除以根号2012加根号2011

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 05:05:02

试求1除以根号2加1加1除以根号3加根号2加...加1除以根号2012加根号2011
试求1除以根号2加1加1除以根号3加根号2加...加1除以根号2012加根号2011

试求1除以根号2加1加1除以根号3加根号2加...加1除以根号2012加根号2011
1/(√2+1)+1/(√3+√2)+.+1/(√2012+√2011)
=(√2-1)/((√2+1)(√2-1))+(√3-√2)/((√3+√2)(√3-√2))+.+(√2012-√2011)/((√2012+√2011)(√2012-√2011))
=(√2-1)+(√3-√2)+.+(√2012-√2011)
=√2012-1