1x1/5+1/5x1/9+1/9x1/13+.+1/2005+1/2009这个式子,后面不是相加吧,是相乘吧,是1/2005X1/2009吧?
1x1/5+1/5x1/9+1/9x1/13+.+1/2005X1/2009
=1/4X(1-1/5)+1/4X(1/5-1/9)+1/4X(1/9-1/13)+.+1/4X(1/2005-1/2009)
=1/4X{1-1/5+1/5-1/9+1/9-1/13+.1/2001-1/2005+1/2005-1/2009}
=1/4X(1-1/2009)
=1/4X(2008/2009)
=502/2009