化简:1/(2+√2)+1/(√6+2)+1/(√8+√6)+…+1/(√2012+√2010)+1/(√2014+√2012)

问题描述:

化简:1/(2+√2)+1/(√6+2)+1/(√8+√6)+…+1/(√2012+√2010)+1/(√2014+√2012)

原式=(1/2)*(2-√2+√6-2+√8-√6+…+√2012-√2010+√2014-√2012)
=(1/2)*(-√2+√2014)=(√2014-√2)/2请问为什么要*1/2呢?绝对是对的!!!!