Question: Let X be a nonnegative random variable. Prove that E[X] (E[X2])1/2 (E[X3])1/3 . . .

Let X be a nonnegative random variable.
Prove that
E[X] ≤ (E[X2])1/2 ≤ (E[X3])1/3 ≤ . . .

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