1∕1×2+1∕2×3……1∕2009×2010得几

问题描述:

1∕1×2+1∕2×3……1∕2009×2010得几

1∕1×2+1∕2×3……1∕2009×2010
=1-1/2 + 1/2-1/3 +1/3-1/4+...+1/2008-1/2009+1/2009-1/2010
=1-1/2010
=2009/2010