deletions | additions       diff --git a/beginproblem_a_You_a.tex b/beginproblem_a_You_a.tex  index 810a54d..c90c498 100644  --- a/beginproblem_a_You_a.tex  +++ b/beginproblem_a_You_a.tex 
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$5(2^k+3^k+4^k)\leq5*5^k$  \\  $5*2^k+5*3^k+5*4^k\leq5*5^k$  \\We can replace each $5$ with the value of the coefficient for each term. This still keeps the inequality true true.  \\  $2*2^k+3*3^k+4*4^k\leq5*5^k$  \\  $2^{k+1}+3^{k+1}+4^{k+1}\leq5^{k+1}$  \\  Therefore, the inequality must hold for $n\geqc$, where $c=3$  \\  \textit{Q.E.D}  \\\\  This implies that $2^n+3^n+4^n = O(5^n)$ because for $n\geqc$, $2^n+3^n+4^n$ is bounded by and never exceeds $5^n$. Therefore, $2^n+3^n+4^n = O(5^n)$.  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.