Question

Closed form of finite Euler sum $\sum_{k=1}^n \frac{ H_{k}}{(2k+1)}$

score 404 · Answer 1 · 2026-03-25 06:06:32

404

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Closed form of finite Euler sum $\sum_{k=1}^n \frac{ H_{k}}{(2k+1)}$

Published on 25 Mar 2026 - 6:06

score 29 · Answer 2 · 2026-03-28 05:58:53

29

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Prove by induction summation with exp index

Published on 28 Mar 2026 - 5:58

score 118 · Answer 3 · 2026-03-25 14:25:32

118

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Show that for positive numbers a,b,c,d, $\sum_{cyc} ab \leq \frac{1}{4}\left(\sum_{cyc} a \right)^2$ and ...

Published on 25 Mar 2026 - 14:25

score 106 · Answer 4 · 2026-03-27 10:47:56

106

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find minimum and maximum value of $ab+cd+ef+gh $ given that$ a,b,c,d,e,f,g,h$ are members in $H$

Published on 27 Mar 2026 - 10:47

score 199 · Answer 5 · 2026-03-25 19:07:15

199

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Calculate $ \biggr\lfloor \frac{1}{4^{\frac{1}{3}}} + \frac{1}{5^{\frac{1}{3}}} + ... + \frac{1}{1000000^{\frac{1}{3}}} \biggr\rfloor$

Published on 25 Mar 2026 - 19:07

score 146 · Answer 6 · 2026-03-26 01:16:40

146

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What are the most elegant approximations of the sum of binomial terms, by using Stirling's approximation?

Published on 26 Mar 2026 - 1:16

score 40 · Answer 7 · 2018-09-10 00:37:25

40

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How do we know that $\sum\limits_{k=1}^n\left(\frac{a}{b}\right)^{k-1}< n $?

Published on 10 Sep 2018 - 0:37

score 334 · Answer 8 · 2026-03-28 01:07:14

334

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Finding the value of an unknown from a summation of an exponential

Published on 28 Mar 2026 - 1:07

score 45 · Answer 9 · 2018-09-10 04:28:34

45

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Show that $\sum_{k=1}^n e^{2\pi i (k-1)(a-b)/n}=0$

Published on 10 Sep 2018 - 4:28

score 285 · Answer 10 · 2026-03-26 14:23:02

285

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Find sum of all integer solution of $\frac{2}{a} + \frac{3}{b} + \frac{4}{c} + \frac{5}{d} = \frac{1}{14}$

Published on 26 Mar 2026 - 14:23

score 336 · Answer 11 · 2026-03-25 17:20:07

336

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How to prove this inequality involving the minimum of two chosen numbers

Published on 25 Mar 2026 - 17:20

score 141 · Answer 12 · 2018-09-10 18:53:57

141

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Can we prove this inequality $1+\sqrt{2}+\cdots+\sqrt{n}<\frac{4n+3}{6}\sqrt{n}$ using integrals by parts?

Published on 10 Sep 2018 - 18:53

score 2k · Answer 13 · 2026-03-22 23:01:30

2k

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Does changing the order of the indices of the Kronecker delta within a summation matter?

Published on 22 Mar 2026 - 23:01

score 103 · Answer 14 · 2026-03-25 14:25:34

103

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a formula for calculating value of interest bearing account to which I make monthly deposits

Published on 25 Mar 2026 - 14:25

score 46 · Answer 15 · 2018-09-11 12:29:49

46

Views

Proving formula for repeated geometric sum

Published on 11 Sep 2018 - 12:29

List Question

Closed form of finite Euler sum $\sum_{k=1}^n \frac{ H_{k}}{(2k+1)}$

Prove by induction summation with exp index

Show that for positive numbers a,b,c,d, $\sum_{cyc} ab \leq \frac{1}{4}\left(\sum_{cyc} a \right)^2$ and ...

find minimum and maximum value of $ab+cd+ef+gh $ given that$ a,b,c,d,e,f,g,h$ are members in $H$

Calculate $ \biggr\lfloor \frac{1}{4^{\frac{1}{3}}} + \frac{1}{5^{\frac{1}{3}}} + ... + \frac{1}{1000000^{\frac{1}{3}}} \biggr\rfloor$

What are the most elegant approximations of the sum of binomial terms, by using Stirling's approximation?

How do we know that $\sum\limits_{k=1}^n\left(\frac{a}{b}\right)^{k-1}< n $?

Finding the value of an unknown from a summation of an exponential

Show that $\sum_{k=1}^n e^{2\pi i (k-1)(a-b)/n}=0$

Find sum of all integer solution of $\frac{2}{a} + \frac{3}{b} + \frac{4}{c} + \frac{5}{d} = \frac{1}{14}$

How to prove this inequality involving the minimum of two chosen numbers

Can we prove this inequality $1+\sqrt{2}+\cdots+\sqrt{n}<\frac{4n+3}{6}\sqrt{n}$ using integrals by parts?

Does changing the order of the indices of the Kronecker delta within a summation matter?

a formula for calculating value of interest bearing account to which I make monthly deposits

Proving formula for repeated geometric sum

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