Calculation: 2 × 4 / 1 + 4 × 6 / 1 + 6 × 8 / 1 +. 2010 × 2012 / 1

Calculation: 2 × 4 / 1 + 4 × 6 / 1 + 6 × 8 / 1 +. 2010 × 2012 / 1

It is easy to use split term method to solve this problem. 1 / N (n + 2) = 1 / 2 * (1 / n-1 / (n-2))
In this way, the question is simplified as: 1 / 2 (1 / 2-1 / 4 + 1 / 4-1 / 6. + 1 / 2010-1 / 2012)
=1/2(1/2-1/2012)
=1005/4024

Clever calculation: 1 / 2 + 1 / 2 + 1 / 3 + 1 / 3 + 1 / 4 + 1 / 2010 + 1 / 2012 = how much

Sum of split term phase elimination method
1 / 2 = 1 / 1-2 / 1
1 / 2 / 3 = 1 / 2-1 / 3
3 / 4 = 1 / 3-1 / 4
……
1 / 2010-1 / 2011 = 1 / 2010-1 / 2011
Then the left and right sides can be added to achieve the interval cancellation

(—2)+4+(—6)+8+...+(—2010)+2012

(—2)+4+(—6)+8+...+(—2010)+2012
=【(—2)+4】+【(—6)+8】+...+【(—2010)+2012】
=2+2+…… +2
=2×503
=1006

1 / 2 + 1 / 6 + 1 / 12 + 1 / 20 + 1 / 30 + 1 / 42 calculate this problem in a simple way

1 /2+1/6+1/12+1/20+1/30+1/42
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7