1 / 1 [1 times 2] + 1 / [2 times 3] + 1 / [3 times 4] + 1 / [4 times 5] + +How much is 1 / [2005 times 2006]

1 / 1 [1 times 2] + 1 / [2 times 3] + 1 / [3 times 4] + 1 / [4 times 5] + +How much is 1 / [2005 times 2006]

1 / 1 [1 times 2] + 1 / [2 times 3] + 1 / [3 times 4] + 1 / [4 times 5] + +1 / [2005 times 2006]
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+…… +1/2004-1/2005+1/2005-1/2006
=1-1/2006
=2005/2006