"Limitless" is a TV adaptation of Bradley Cooper's movie with the same title released back in 2011. The series just like the movie is based on a pill that gives limitless brain powers to a person.
The opening scene of the series shows Brian Finch played by Jake McDorman running in the Union Square chased by some guys. At one point, men in trench coats that were chasing lose Finch confused by the layout of the Union Square. However Rebecca Harris played by Jennifer Carpenter manages to catch up with Finch. To escape from Harris who is from the FBI Finch jumps onto the train track and is almost hit by an L train, according to Vulture.
Coming to Finch, an aimless person from a family where all the members other than him are very successful. Finch, though not a full-time musician is in a band and does part-time clerical work in a bank. When Finch tries to explain his new musical project to his family members in the dinner table his father collapses of a mysterious illness.
Finch who is devastated meets his friend Eli for lunch and explains everything that is going on in his life. Eli who is an investment banker tells his good old friend that he might be able to help. He opens a small case, takes a pill out of it and hands it over to Finch.
Finch finds nothing miraculous as soon as he has the pill but after a while in the bank it does. The "Limitless" pill the way Eli calls it works this way: "Your brain is a miracle, but it's not efficient. There's a maze inside everyone's head, a labyrinth of missed connections and untapped potential. But now suddenly, I had access to every single brain cell."
The pill does super miracles that Finch could accomplish his task at bank with ease, diagnose his dad's mysterious illness, plays speed chess meanwhile advises his boss to break-up with her boyfriend and pursue an MBA.
The limitless pill however doesn't work for long and therefore he looks for his friend Eli for another dose. He finds Eli shot dead in his apartment but manages to find his pill by the time the police arrived the spot. After a chase the prior mentioned train incident happens at the end of which Finch meets up with the senator played by Cooper.