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Hint: By hand, find the smallest $c$ for which $n=c$ satisfies this inequality, and  then prove by induction that it holds for all $n \ge c$.  \end{problem}  \\ \\\\  \textbf{Solution 2: }  \\*  Base Case: For $n=3$ $2^3+3^3+4^3\leq5^3$