4/(1×5)+4/(5×9)+4/(9×13)+.....+4/(2004×2008)=
=(5-1)/(1×5)+(9-5)/(5×9)+(13-9)/(9×13)+......+(2008-2004)/(2004×2008)=
=5/(1×5)-1/(1×5)+9/(5×9)-5/(5×9)+13/(9×13)-9/(9×13)+.....+
+2008/(2004×2008)-2004/(2004×2008)=
=1/1-1/5+1/5-1/9+1/9-1/13+1/13+....-1/2004+1/2004-1/2008=
=1/1-1/2008=
=2008/2008-1/2008=2007/2008
