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A BEAST of a series - are you ready?

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Mu Prime Math

Mu Prime Math

Күн бұрын

Identity with (n-1) choose w: • Binomial Coefficients ...
Beta function integral: • Proving an Integral Fo...
Fematika's solution: • An ABSOLUTELY ASTONISH...
A math competition problem from Hong Kong. We'll need every trick in the book to solve this one!
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Пікірлер: 48
@blackpenredpen
@blackpenredpen 5 жыл бұрын
Yes, he is serious! At 13:09, that’s the biggest telescoping sum that I have ever seen.
@vijaybala7813
@vijaybala7813 5 жыл бұрын
yes it is true
@Fematika
@Fematika 5 жыл бұрын
Wow, this is extremely different from what I did! It is really cool to see how this can be done with a completely different method.
@kenhaley4
@kenhaley4 5 жыл бұрын
When you started I thought it was going to be a quick trick. Not so quick, but still my jaw dropped. That was quite a show. Amazing. Thank you.
@blackpenredpen
@blackpenredpen 5 жыл бұрын
Ken Haley When he got that integral and the used the beta function, I was like “Whoa!!!!”
@MG-hi9sh
@MG-hi9sh 5 жыл бұрын
@@blackpenredpen I too am an admirer of it, but it's a shame I've only just woken up. I can't register most of his method rn. 😂😂😂
@shanmugasundaram9688
@shanmugasundaram9688 4 жыл бұрын
So many tricks.Converting the terms of the series to factorials,partial fractions.calculaing the coefficients, converting the infinite summation to a finite summation ,changing to Binomial coefficients, changing to the integration of a polynomial, Magical conversion to Beta function and finally a generalization to similar series.In every step of the proof a trick is involved.Very interesting.
@chirayu_jain
@chirayu_jain 5 жыл бұрын
23:23 here comes the beta function
@guillemordi3725
@guillemordi3725 5 жыл бұрын
That was crazy! Amazing job
@QuotientGD
@QuotientGD 5 жыл бұрын
I come from HK and have joined this competition for several years. Never seen anything as tough as this haha
@nikned27th74
@nikned27th74 5 жыл бұрын
I am proud to be one of your first subs
@andreapaps
@andreapaps 3 жыл бұрын
Watching this video from Hong Kong :D ... Time to find out where the competition is I guess
@mountainc1027
@mountainc1027 5 жыл бұрын
And here I thought that failing the preliminaries was my fault for not practising hard enough... The main event is really tough!!
@Tomaplen
@Tomaplen 5 жыл бұрын
17!/76! = (17/76)! you factor by factorial and then its trivial...
@mollaconan
@mollaconan 4 жыл бұрын
It's like watching a wonderful movie over and over again an enjoying it, even though you know every scene and the ending! That is what I do.
@blue_blue-1
@blue_blue-1 5 жыл бұрын
At least 57! kudos! Because I really couldn´t follow up you solution.
@Archipelago.
@Archipelago. 4 жыл бұрын
Partial fraction ; just go ahead with bprp's hiding method !! 😍 To mu prime : such a crystal clear voice , I loved this video 🇮🇳🇮🇳 Watching from india ✌️
@paulhaso
@paulhaso 5 жыл бұрын
Ok, this was awesome
@BluePi3142
@BluePi3142 5 жыл бұрын
Holy cow those partial fractions. Very nice video!
@AndDiracisHisProphet
@AndDiracisHisProphet 5 жыл бұрын
nice
@yatharthgupta6468
@yatharthgupta6468 3 жыл бұрын
You could simple make it a telescoping series by writing 1 in numerator as [(k+59)-(k+1)]/58 ....just a one minute solution..
@AsadullahJamalFaizi
@AsadullahJamalFaizi 5 жыл бұрын
Awesome dude love from India
@tonk6812
@tonk6812 5 жыл бұрын
Cool...nice voice 😎😎..keep on going..
@ortho5387
@ortho5387 4 жыл бұрын
Constructive suggestion:try to write little neat
@BabuRaviranjan
@BabuRaviranjan 4 жыл бұрын
No way ... Mathematics will become so tough to understand if u follow such methods
@chirayu_jain
@chirayu_jain 5 жыл бұрын
18:51 I saw that video 😃😃
@user-gl3yh3jf5h
@user-gl3yh3jf5h 5 жыл бұрын
proof or disprove: n/(n+m) + n(n+1) / (n + m)(n + m + 1) + ... (e.g. the general form of the sum) is equal to n/(n + m)m
@Dionisi0
@Dionisi0 5 жыл бұрын
I came here because of blackpenredpen, well done sir
@electrovector7212
@electrovector7212 5 жыл бұрын
Me too
@blackpenredpen
@blackpenredpen 5 жыл бұрын
👋 thank you for the supports!!
@user-gc1dw3ks4s
@user-gc1dw3ks4s 4 жыл бұрын
Art
@gregoriousmaths266
@gregoriousmaths266 4 жыл бұрын
Wow isn’t that the one that fematika also did? Really cool method btw
@silvanomicele1373
@silvanomicele1373 4 жыл бұрын
Mega telescope. I like it
@L4wLiP0p
@L4wLiP0p 5 жыл бұрын
Now does this hold in general, i.e. if we start from k in the numerator and m(m+1) in the denominator, does the resulting sum converge to k/(m(m-k))? I would assume the steps generalize pretty nicely since at no point did you really use the values.
@MuPrimeMath
@MuPrimeMath 5 жыл бұрын
I think you're right!
@quantumsigmaqed6312
@quantumsigmaqed6312 5 жыл бұрын
Take (58*75/17)S = 58/76 + 18*58/76*77 + 18*19*58/76*77*78 + 18*19*20*58/76*77*78*79 + … = (76-18)/76 + 18*(77-19)/76*77 + 18*19*(78-20)/76*77*78 + 18*19*20*(79-21)/76*77*78*79 +… = 76/76 - 18/76 + 18*77/76*77 - 18*19/76*77 + 18*19*78/76*77*78 - 18*19*20/76*77*78 + 18*19*20*79/76*77*78*79 - 18*19*20*21/76*77*78*79 + … = 1 Any starting value does the same, so yes, that's the pattern
@mafprivate8841
@mafprivate8841 5 жыл бұрын
I want to say that I come from HK and I participate this competition this year but it is even for F1 ! So you can do this without using hard techniques actually
@quantumsigmaqed6312
@quantumsigmaqed6312 5 жыл бұрын
For those with different systems Form 1 = Grade 7/ Year 8
@quantumsigmaqed6312
@quantumsigmaqed6312 5 жыл бұрын
Plus you have only 6 mins for each q on average
@nevokrien95
@nevokrien95 5 жыл бұрын
Can u do this for a genral n
@MuPrimeMath
@MuPrimeMath 5 жыл бұрын
It is possible, but it takes a little longer!
@yaleng4597
@yaleng4597 5 жыл бұрын
Wait, but the answer key says that the answer is 1/1275
@angelmendez-rivera351
@angelmendez-rivera351 4 жыл бұрын
Then the answer key is wrong
@blackloop1861
@blackloop1861 5 жыл бұрын
yay
@jannesl9128
@jannesl9128 4 жыл бұрын
I have no friends which like math :(
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