Question

Why is $O(\sum_{n=1}^\infty \frac{\log n}{n^c}) = O(\int_1^\infty \frac{\log w}{w^c}dw)?$

score 19 · Answer 1 · 2022-01-07 19:57:41

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Why is $O(\sum_{n=1}^\infty \frac{\log n}{n^c}) = O(\int_1^\infty \frac{\log w}{w^c}dw)?$

Published on 07 Jan 2022 - 19:57

score 19 · Answer 2 · 2026-03-24 05:45:12

19

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score 19 · Answer 3 · 2026-03-24 05:45:13

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score 19 · Answer 4 · 2021-12-30 19:22:46

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score 19 · Answer 5 · 2021-12-20 04:58:21

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score 19 · Answer 6 · 2021-12-19 01:12:34

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score 19 · Answer 7 · 2026-03-30 01:47:07

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Views

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score 19 · Answer 8 · 2026-02-24 05:27:14

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score 19 · Answer 9 · 2021-12-13 11:36:04

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score 19 · Answer 10 · 2026-03-24 07:15:43

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score 19 · Answer 12 · 2026-03-24 07:15:43

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score 19 · Answer 14 · 2021-12-05 20:23:28

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score 19 · Answer 15 · 2026-03-24 07:15:43

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List Question

Why is $O(\sum_{n=1}^\infty \frac{\log n}{n^c}) = O(\int_1^\infty \frac{\log w}{w^c}dw)?$

Showing that $([0,1),\rm d)$ is compact where $\mathrm{d}(x,y)=|\exp(2\pi i\cdot x)-\exp(2\pi i\cdot y)|$ - is my proof correct?

Simplest optimization method for specific nonlinear function

Looking for papers / terminology on binary array guessing game problem

Question on a mutiple improper integral

Can a transcendental functional of a PSD matrix have different eigenvectors?

A smooth $Q \in \mathbb R^N \to \mathbb R$ close to, but strictly below min

Is it possible for a DPDA(deterministic pushdown automaton) to have both transitions: (q, aw, xyz) -> (q, w, yz) and (q, bw, xyz) -> (q1, bw, xyz)?

Are these formulations of lagrange multiplier theorem equivalent?

Extracting countably many subnets from a net

The U-Box-It store carries boxes in four sizes. The tables below show the four sizes of storage boxes the store sells and the revenues ...

Is the following simplification of the running time of an algorithm given in Big-O notation correct?

Finding D1 and g for the following equation - infinite series question

Bounding exponentiation functions with floor and ceiling functions as exponents.

Calculating the cardinality of the set of integers accumulated by maximum

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