Question

1/n - 1/n+1 = ?

1/1*2+1/2*3+1/3*4+....+ 1/2007*2008+1/2008*2009+1/2009*2010 = ?

Answer 1

1/n+1 = 1/n(n+1)

1/1*2+1/2*3+1/3*4+....+ 1/2007*2008+1/2008*2009+1/2009*2010 =

= 1- 1/2010 =2009/2010

Answer 2

1/n - 1/(n+1) = 1/[n(n+1)]
1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +...........+1/2009 - 1/2010 = 1/1 - 1/2010 =
= 2009 /2010