Official TSR Mathematical Society

Scroll to see replies

Daniel Freedman

I'll give credit to the source of this afterwards, as the solution is on there too.

For all real x, evaluate

\displaystyle \sum_{r=0}^{\infty} \frac{\sin^3{(3^r x)}}{3^r}

never done such a limit with any trig or infact never seen one until now.

some kind of tip?

Reply 1321

Daniel Freedman

DeanK22

never done such a limit with any trig or infact never seen one until now.

some kind of tip?

Presumably you've writted out the first few terms and aren't getting anywhere?

A good idea with summations is to try and express the general term in a nicer form that you can sum.

Reply 1322

Lysdexia

DeanK22

You are pondering over a question that makes absolutely no sense - 2 is a symbol specifying an amount yet we could have arbitarly chosen another amount [i.e. in our conventional view of numbers we could have gone from 1 object to three objects with no 2 objects represented by a whole number].

I thought it would be something like that! :wink:

Reply 1323

SimonM

Daniel Freedman

I'll give credit to the source of this afterwards, as the solution is on there too.

For all real x, evaluate

\displaystyle \sum_{r=0}^{\infty} \frac{\sin^3{(3^r x)}}{3^r}

Very nice question. My first though was **** me that looks bitchy

Spoiler

Reply 1324

GoodbyeTSR

SimonM

Very nice question. My first though was **** me that looks bitchy

Spoiler

Telescopes nicely. :smile:

Offtopic: Is University of Leicester good for math? I just got an offer.

Reply 1325

Oh I Really Don't Care

SimonM

Very nice question. My first though was **** me that looks bitchy

Spoiler

how have you taken the sum?

Reply 1326

Oh I Really Don't Care

thomaskurian89

Telescopes nicely. :smile:

Offtopic: Is University of Leicester good for math? I just got an offer.

...

... yeah it is good - maths staff (one of them) recieved his degree from there and spoke highly - it is currently an active place for new professors because of ssome kind of scholarship they have in place - apparently some very talented.

Reply 1327

Oh I Really Don't Care

DeanK22

how have you taken the sum?

????

Reply 1328

Daniel Freedman

DeanK22

how have you taken the limit?

\displaystyle \sum_{r=0}^{n}{\frac{\sin^3(3^{r} x)}{3^r}}=\frac{1}{4}\sum_{r=0}^{n} \frac{3\sin(3^r x)-\sin(3^{r+1}x)}{3^r}=\frac{3}{4}\sin x-\frac{1}{4}\frac{\sin(3^{n+1}x)}{3^n}

Now let n tend to infinity, and the second expression vanishes.

Unparseable latex formula:

\bigstar \boxed{ \mbox{Nicely done, Simon [s]smile[/s]}} \bigstar

Reply 1329

SimonM

Daniel Freedman

Unparseable latex formula:

\bigstar \boxed{ \mbox{Nicely done, Simon [s]smile[/s]}} \bigstar

Thanks, (just got home)

Sauce?

Reply 1330

Oh I Really Don't Care

... vm appreciated

\mu on

rather oddly the smiley face looks really scary though :yep:

Reply 1331

The Muon

DeanK22

... vm appreciated

\mu on

rather oddly the smiley face looks really scary though :yep:

Anytime.

p.s. I prefer

\mu^-

Reply 1332

Oh I Really Don't Care

... Prove

\displaystyle tan(A)tan(B)tan(C) = tan(A) + tan(B) + tan(C)

\displaystyle A + B + C = \pi

Reply 1333

Daniel Freedman

DeanK22

... Prove

\displaystyle tan(A)tan(B)tan(C) = tan(A) + tan(B) + tan(C)

\displaystyle A + B + C = \pi

Very similar to a question we've had before.

Spoiler

Reply 1334

h4r5h

Hi, I couldn't find any thread for past papers, so I'm just gonna post my query here..

Does anyone know where I can get my hands on M3 and M4 past papers? Solomons too would be very helpful, but I have no idea where to get them from. (Btw, don't say school! Is there anywhere else?)

Reply 1335

h4r5h

Merci, Merci beaucoup!

Reply 1336

Adjective

Sue and Bob take turns rolling a 6-sided die. Once either person rolls a 6, the game is over. Sue rolls first. If she doesn’t roll a 6, Bob rolls the die; if he doesn’t roll a 6, Sue rolls again. They continue taking turns until one of them rolls a 6.

Bob rolls a 6 before Sue.

What is the probability Bob rolled the 6 on his second turn?

(from xkcd)

Spoiler

SimonM

Spoiler

Forgive this stupid question, but does it mean 'what is the probability Bob rolled the 6 on his second roll, given that he rolls a 6 before Sue?' If so, I don't see why it's not just:

Spoiler

If I'm not understanding this right, could you please explain it?