My Generous Uncle

Calculus Level 2

My uncle says he'll deposit some money into my bank account. He'll deposit \(x\) (where \(x < 2\)) dollars on the first day, \(\dfrac{x^2}{2}\) dollars on the second day, \(\dfrac{x^3}{4}\) dollars on the third day, \(\dfrac{x^4}{8}\) dollars on the fourth day, and so on forever.

Which expression represents the amount of money that will be delivered into my bank account?

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