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NICK CARTER Serenades Terminally Ill Fan

Nick Carter made a dying fan's wish come true ... singing the Backstreet Boys' signature hit directly to her in a real tearjerker moment.

TMZ obtained the super touching video recorded in Frankfurt, Germany ... as the singer makes his way through the crowd, goes straight in to hug terminally ill Jenni Schmidt and then begins singing "I Want It That Way" -- just for her.

Jenni, whose last wish was made possible by an org named, Der Wünschewagen, was clearly over the moon during Nick's "Who I Am" world tour last Sunday.

You can see how she was gripping Nick’s hand, and singing along to the lyrics while he was totally focused on making her feel special.

The crowd got in on the sing-along, making it even more amazing for 40-year-old Jenni, who tells TMZ she’s been a Backstreet Boys fan since 1995.

In fact, she's been to a handful of their concerts, and has already met the guys in band a few times before.

Jenni says, "The moment when Nick stood next to me and sang this wonderful song was such a heartwarming moment. I never believed this moment would come."

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