Calculati:1/1×2+1/2×3+1/3×4+...+1/2007×2008+1/2008×2009+1/2009×2010

Răspuns :

=1/1-1/2+1/2-1/3+...+1/2009-1/2010
Reducând termenii, obțin:
=1/1-1/2010=
=2010/2010-1/2010=
=2009/2010