化簡(4/(√2+2)+4/(2+√6)+4/(√6+√8)+…+4/(√2012+√2014)(√2014+√2)

化簡(4/(√2+2)+4/(2+√6)+4/(√6+√8)+…+4/(√2012+√2014)(√2014+√2)

=2(2-√2)+2(√6-2)+2(√8-√6)+……+2(√2014-√2012)
-2(√2014-√2)