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Today, 07:48

Opalg replied to a thread nth term with fractions in Pre-Algebra and Algebra

Not just for the next term, but for the whole sequence! In fact, your prediction and mine both say that the $(n+1)$th term minus the $n$th term is...

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8 replies | 105 view(s)
Today, 06:37

Opalg replied to a thread nth term with fractions in Pre-Algebra and Algebra

Hi hm2018April, and welcome to MHB! Mathematicians hate problems like this, because there usually isn't a single, "correct" solution. You need to...

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8 replies | 105 view(s)
Yesterday, 08:57

Opalg replied to a thread Challenge problem #2 [Olinguito] in Challenge Questions and Puzzles

Let $A = \begin{bmatrix}0&1\\1&1\end{bmatrix} = \begin{bmatrix}\varphi_0&\varphi_1\\ \varphi_1&\varphi_2\end{bmatrix}$. By induction, $A^n =...

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2 replies | 58 view(s)
April 22nd, 2018, 10:17

MarkFL replied to a thread Olinguito in Introductions

Hello, and welcome to MHB! (Wave)

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8 replies | 102 view(s)
April 22nd, 2018, 09:57

Opalg replied to a thread Banach space in Analysis

$$|f_n(x)-f_m(x)|=\left| \frac{\sin^2\left (\frac{2\pi}{T}x\right )}{\frac{1}{n}+\left |\sin\left (\frac{2\pi}{T}x\right )\right |}-\frac{\sin^2\left...

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6 replies | 78 view(s)
April 22nd, 2018, 04:36

Opalg replied to a thread Challenge problem #1 [Olinguito] in Challenge Questions and Puzzles

Hi Olinguito, and welcome to MHB! We look forward seeing your problems. $2x^2y^2-2xy+x^2+y^2-2x-2y+3 = 2(xy-1)^2 + (x+y-1)^2$. If that is zero then...

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4 replies | 69 view(s)
April 22nd, 2018, 04:19

Opalg replied to a thread
Unsolved Challenge
imaginary integral in Challenge Questions and Puzzles

Rationalise the fraction: \frac{\sin t}{ \sin t+ i\sqrt{n+\cos^2 t}} = \frac{\sin t\bigl( \sin t - i\sqrt{n+\cos^2 t}\bigr)}{1+n}.

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1 replies | 57 view(s)
April 21st, 2018, 16:02

Opalg replied to a thread Error 502, bad gateway in Questions, Comments, and Feedback

Reminds me of a recent xkcd cartoon.

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19 replies | 514 view(s)
April 21st, 2018, 14:15

MarkFL replied to a thread Error 502, bad gateway in Questions, Comments, and Feedback

There was no inconvenience, except to you trying to post and to those trying to read the thread. It was bad coding on my part, done before I knew the...

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19 replies | 514 view(s)
April 20th, 2018, 22:16

MarkFL replied to a thread BBCode For Username HTML Markup in vBulletin Products

Update - Version 1.3.1: Bug fix for usernames with special characters.

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2 replies | 224 view(s)
April 20th, 2018, 19:16

MarkFL replied to a thread Error 502, bad gateway in Questions, Comments, and Feedback

I have added code to that external script so a single quote in a username won't throw an error, and I edited the post so that only the username is...

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19 replies | 514 view(s)
April 20th, 2018, 12:00

MarkFL started a thread Problem Of The Week #310 Apr 20th, 2018 in POTW for Secondary School/High School Students

Here is this week's POTW: A small bug is placed between two blocks of masses $m_1$ and $m_2$ ($m_1>m_2$) on a frictionless table. A horizontal...

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0 replies | 38 view(s)
April 20th, 2018, 11:59

MarkFL replied to a thread Problem Of The Week #309 Apr 12th, 2018 in POTW for Secondary School/High School Students

No one answered this week's problem, and my solution is as follows: A formula for power $P$ we can apply here is: P=\frac{1}{2}\mu\omega^2A^2v...

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1 replies | 75 view(s)
April 17th, 2018, 10:04

Opalg replied to a thread Most ever users in Chat Room

It looks as though Spring Break has brought out the users again! It now says Most users ever online was 439, April 15th, 2018 at 19:20.

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2 replies | 321 view(s)
April 17th, 2018, 03:51

Opalg replied to a thread Finding last digits of 983389^389 in Number Theory

Hi Alexthexela, and welcome to MHB! In the number $983,389^{389}$, the base is $983,389$ and the exponent is $389$. The problem tells you to...

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1 replies | 94 view(s)
April 16th, 2018, 12:25

Opalg replied to a thread Compute \, S^k k=2,...,6 in Linear and Abstract Algebra

In the UK, it is the leading supplier of accounting software packages for small businesses, https://uk.sageone.com/accounts/. I would not...

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7 replies | 119 view(s)
April 15th, 2018, 20:01

MarkFL replied to a thread A Difficult Partial Sum in Pre-Calculus

Awesome work, as always Chris! (Yes) Using your post, where the base case and induction statement have been given, then the induction step would...

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6 replies | 133 view(s)
April 15th, 2018, 13:59

Opalg replied to a thread A Difficult Partial Sum in Pre-Calculus

Writing those as $$S_0= \frac 14 = \frac12 - \frac14 = \frac12 - \frac28 = \frac12 - \frac{2^1}{3^{2^1} - 1}, \\ S_1= \frac 9{20} = \frac12...

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6 replies | 133 view(s)
April 15th, 2018, 12:02

MarkFL replied to a thread A Difficult Partial Sum in Pre-Calculus

Here are the choices: A.) \frac{1}{2} B.) \frac{1}{2}-\frac{2^{2006}}{3^{2^{2006}}-1} C.) \frac{1}{2}-\frac{2^{2005}}{3^{2^{2005}}-1} D.)...

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6 replies | 133 view(s)
April 14th, 2018, 10:56

MarkFL replied to a thread A Difficult Partial Sum in Pre-Calculus

The actual sum he's given is: S=\sum_{k=0}^{2006}\left(\frac{2^k}{3^{2^k}+1}\right) And he's given several choices for the result. I was hoping...

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6 replies | 133 view(s)
April 14th, 2018, 10:10

MarkFL started a thread A Difficult Partial Sum in Pre-Calculus

Hello MHB! (Wave) A young man in high school I know has been essentially tasked with finding the following partial sum: ...

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6 replies | 133 view(s)
April 12th, 2018, 11:47

MarkFL replied to a thread Hello from Pan in Introductions

Hello, and welcome to MHB panpan! (Wave)

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6 replies | 94 view(s)
April 12th, 2018, 11:15

MarkFL started a thread Problem Of The Week #309 Apr 12th, 2018 in POTW for Secondary School/High School Students

Hello, MHB Community! (Wave) anemone has asked me to stand in for her for a few weeks, so please be gentle. (Bigsmile) Here is this week's...

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1 replies | 75 view(s)
April 12th, 2018, 11:11

MarkFL replied to a thread Problem Of The Week #308 Apr 6th, 2018 in POTW for Secondary School/High School Students

Hello MHB Community! (Wave) I am going to stand in for anemone for a few weeks. Congratulations to the following for their correct submissions:...

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1 replies | 133 view(s)
April 9th, 2018, 21:16

MarkFL replied to a thread Deduction in Discrete Mathematics, Set Theory, and Logic

Yes, that was a bad post. The OP stated an unfamiliarity with limits, so I "winged it." What I would actually do is: ...

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7 replies | 108 view(s)

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We are an online community that gives free mathematics help any time of the day about any problem, no matter what the level. You will have to register before you can post. To start viewing messages, select the forum that you want to visit from the selection below.

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