ISI 2016 B.Math Entrance(1)

Calculus Level 3

For \(\alpha \in \left(0,\dfrac{3}{2}\right)\), define \(x_n = (n+1)^{\alpha}-n^{\alpha}\).

What are all the possible values of \(\displaystyle{\lim_{n \rightarrow \infty} x_n}\)?

Note: If you think that the limit can also diverge to infinity, then choose the option with \(\infty\) as well.

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