A calculus problem by Snehal Shekatkar

Calculus Level 3

Consider the following series:

\[\sum_{n=1}^{\infty}\left(\frac{n-1}{n}\right)^{n} = 0 + \left(\frac{1}{2}\right)^{2}+ \left(\frac{2}{3}\right)^{3} + \cdots \]

Which of the following statements is true for the series above?

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