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.

×