Does $E[X_n^k]<\infty$ for $k>0$ imply $E[X_n^k]=b$ for some real $b$?

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If you see that $E[X_{n}^k] < \infty$ for $k > 0$ (where $X_n^k$ is a random variable), is it safe to assume that $E[X_{n}^k]=b$ for some $b \in R$ (reals)?