In a blender or food processor puree 1 cup of the raspberries with 1 cup of water and force the puree through a fine sieve set over a pitcher pressing hard on the solids
Add remaining 1 cup of raspberries and remaining 2 12 cups of water the sugar and the lime juice
Stir mixture until sugar is dissolved
Divide the limeade among tall glasses fill with ice cubes and garnish each drink with mint sprigs