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Results tagged with inequalities
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user 110426
for questions involving inequalities, upper and lower bounds.
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Most elementary proof showing that exponential growth wins against polynomial growth
For some fixed positive integer $k$, let $n^k < 2^n < n^{k+1}$
Now if we go from $n$ to $n+1$ and take ratios we get:
$\frac{2^{n+1}}{2^n} = 2 > \frac{(n+1)^{k+1}}{n^{k+1}}= \left(1 + \frac{1}{n}\righ …