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Inquiry on big $O$ notation

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#algebra-precalculus #limits #asymptotics
1.3k
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Order of growth of logarithms, compared to linear

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#logarithms #asymptotics
44
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Show that $\lim_{n\rightarrow \infty} (1-\omega(\frac{1}{n}))^n=0$ and $\lim_{n\rightarrow \infty} (1-o(\frac{1}{n}))^n=1$

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#sequences-and-series #asymptotics
59
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Analyze for loop with if statement

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#asymptotics
24.8k
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Is it true that $ f(n) = O(g(n))$ implies $g(n) = O(f(n))$

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#asymptotics
151
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What is the probability that two random permutations have same order?

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#combinatorics #discrete-mathematics #permutations #asymptotics #symmetric-groups
288
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Sequence bounded away from $0$ and $2$

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#sequences-and-series #limits #asymptotics
38
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Implications of $n a_n=O((n^{\frac{1}{\alpha}}|b_n|)^\alpha)$

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#sequences-and-series #limits #asymptotics #weak-convergence
119
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Bounded away sequence implications

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#sequences-and-series #limits #asymptotics
81
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Big-Theta - asymptotic bound - is solution sufficient enough?

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#asymptotics
75
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Can you get a closed-form for $\sum_{j=0}^{\infty}\frac{2^{2j-1}B_{2j}}{(2j)!}$?

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#sequences-and-series #asymptotics #bernoulli-numbers
53
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$a_n\geq b_n$ for $n>\bar{n}$ implies $\limsup_{n\rightarrow \infty}a_n\geq \limsup_{n\rightarrow \infty}b_n$

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#sequences-and-series #limits #asymptotics
1.1k
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Prove that $\sum_{i=0}^{k} \lg \frac{n}{2^i} = \Theta(\lg^2 n)$

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#discrete-mathematics #algorithms #logarithms #asymptotics
70
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Proof based on definition of big-$O$

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#asymptotics
126
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Prove or Disprove Θ

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#asymptotics

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