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\\*  Base Case: For $n=3$, $2^3+3^3+4^3 \leq 5^3 = 99 \leq 125$. The inequality holds true for $n=3$  \\  Assume: $2^k+3^k+4^k\leq5^k$. We must show that $k+1$, $2^{k+1}+3^{k+1}+4^{k+1}\leq5^{k+1} $2^{k+1}+3^{k+1}+4^{k+1}\leq5^{k+1}$  To submit the homework, you need to upload the pdf file into ilearn by 8AM on Tuesday,  January 21, and turn-in a paper copy in class.