Question

Prove $\forall k\geq 4,\log(1+x_k)-x_k\leq {-1\over6k}$ where $x_k={(-1)^k\over\sqrt k}$

score 51 · Answer 1 · 2026-03-27 03:44:10

51

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Prove $\forall k\geq 4,\log(1+x_k)-x_k\leq {-1\over6k}$ where $x_k={(-1)^k\over\sqrt k}$

Published on 27 Mar 2026 - 3:44

score 128 · Answer 2 · 2026-04-02 04:53:06

128

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How is the logarithm of an exponential function having a fractional term performed?

Published on 02 Apr 2026 - 4:53

score 53 · Answer 3 · 2019-06-19 08:29:45

53

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using chain rule and logarithms to differentiate a function

Published on 19 Jun 2019 - 8:29

score 140 · Answer 4 · 2026-03-27 04:21:10

140

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Show that $\prod \bigl(1+{i\over n}\bigr)$ diverges.

Published on 27 Mar 2026 - 4:21

score 87 · Answer 5 · 2019-06-19 20:13:50

87

Views

How to solve $x^\sqrt x=\frac{3x}{2}$?

Published on 19 Jun 2019 - 20:13

score 128 · Answer 6 · 2019-06-19 23:12:07

128

Views

Upper bound of natural logarithm for expression close to 1

Published on 19 Jun 2019 - 23:12

score 447 · Answer 7 · 2026-03-29 20:39:36

447

Views

Give geometric proof of $\ln(xy) = \ln x + \ln y$ based on below diagram and please explain it

Published on 29 Mar 2026 - 20:39

score 825 · Answer 8 · 2019-06-20 17:47:44

825

Views

Tight bound for $e^{\sqrt{\log n}}$

Published on 20 Jun 2019 - 17:47

score 59 · Answer 9 · 2019-06-20 19:34:17

59

Views

Does $\forall i\in \mathbb Z^+:\left \lfloor log_{2}(i) \right \rfloor = \left \lfloor log_{2}(i+0.999999) \right \rfloor$

Published on 20 Jun 2019 - 19:34

score 47 · Answer 10 · 2026-03-25 19:00:26

47

Views

Log Properties for Harmonic Numbers

Published on 25 Mar 2026 - 19:00

score 17 · Answer 11 · 2019-06-21 11:59:32

What would be the upper bounds on the accuracy of the algorithm in the below link based on the precision used in the arithmetic operations.

score 22.9k · Answer 12 · 2026-04-02 04:50:02

22.9k

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Change of Base Formula for Exponents

Published on 02 Apr 2026 - 4:50

score 320 · Answer 13 · 2019-06-22 09:23:00

320

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Prove $\log|e^z-z|\leq |z|+1$

Published on 22 Jun 2019 - 9:23

score 102 · Answer 14 · 2026-03-31 03:39:08

102

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Determine the numbers of solutions of equations $\sin v= \frac{v}{1964}$ and $\sin v= \log_{100} v$ .

Published on 31 Mar 2026 - 3:39

score 177 · Answer 15 · 2019-06-23 16:00:25

177

Views

Prove the Napier Logarithm rules

Published on 23 Jun 2019 - 16:00

List Question

Prove $\forall k\geq 4,\log(1+x_k)-x_k\leq {-1\over6k}$ where $x_k={(-1)^k\over\sqrt k}$

How is the logarithm of an exponential function having a fractional term performed?

using chain rule and logarithms to differentiate a function

Show that $\prod \bigl(1+{i\over n}\bigr)$ diverges.

How to solve $x^\sqrt x=\frac{3x}{2}$?

Upper bound of natural logarithm for expression close to 1

Give geometric proof of $\ln(xy) = \ln x + \ln y$ based on below diagram and please explain it

Tight bound for $e^{\sqrt{\log n}}$

Does $\forall i\in \mathbb Z^+:\left \lfloor log_{2}(i) \right \rfloor = \left \lfloor log_{2}(i+0.999999) \right \rfloor$

Log Properties for Harmonic Numbers

What would be the upper bounds on the accuracy of the algorithm in the below link based on the precision used in the arithmetic operations.

Change of Base Formula for Exponents

Prove $\log|e^z-z|\leq |z|+1$

Determine the numbers of solutions of equations $\sin v= \frac{v}{1964}$ and $\sin v= \log_{100} v$ .

Prove the Napier Logarithm rules

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