Simplification (4 / (√ 2 + 2) + 4 / (2 + √ 6) + 4 / (√ 6 + √ 8) +... + 4 / (√ 2012 + √ 2014) (√ 2014 + √ 2)

Simplification (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)