Using sugar syrup is key to making lemonade that is evenly sweetened and has no undissolved sugar at the bottom.
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In a small saucepan, combine the 3/4 cup of water with the sugar. Bring to a boil, then simmer until the sugar is dissolved. Remove from the heat and let the syrup cool to room temperature.
In a large pitcher, combine the remaining 2 quarts of water with the lemon juice and sugar syrup. Add the lemon slices and refrigerate until chilled. Serve the lemonade over ice.