Suppose that the sequence of random variable converges in probability to zero, $X_n=o_p(1)$. How can I show that $$P(\lvert e^{X_n}-1\rvert>c)\to 0, \text{ as } n\to\infty, \forall c>0?$$
Help me if you have any hint. Thanks in advance.
2026-04-26 01:27:16.1777166836
convergence in probability of random variable
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