1+(1/2-1)+(1/4-1/3)+(1/5-1/4)+……+(1/2009-1/2008)+(1/2010+1/2009) 简便计算啊

问题描述:

1+(1/2-1)+(1/4-1/3)+(1/5-1/4)+……+(1/2009-1/2008)+(1/2010+1/2009) 简便计算啊

1+(1/2-1)+(1/4-1/3)+(1/5-1/4)+……+(1/2009-1/2008)+(1/2010+1/2009)
=1-1+1/2-1/2+1/3+……+1/2008-1/2009+1/2009+1/2010
=1/2010