WASHINGTON — The developer of Lumosity “brain training” games will pay $2 million to settle federal allegations that it misled customers about the cognitive benefits of its online apps and programs.

Lumosity is one of the most visible services in the burgeoning brain training industry, which has estimated sales of over $1 billion US per year, according to trade publications.

Lumosity is one of the most visible services in the burgeoning brain training industry, which has estimated sales of over $1 billion per year, according to trade publications. Under federal law ...

Lumosity has logged 20 million overall downloads, and its updated iPhone version, which launched last month, has been used to play 21.5 million mobile brain games.