Another Silly puzzle
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1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 ...... When will the sum of this series exceed 100 ? Will it EVER ? For the thinkers, Why does a candle extinguishes when we blow on it? (Never paid attention to it, right?) Looks simple but it isn't ! * you are right, this guy has got nothing to do... but if you read this we are in the same boat --- My Unedited article^
OK lets divide it in two parts Question 1
Quartz... wrote:
When will the sum of this series exceed 100 ?
Question 2
Quartz... wrote:
Will it EVER ?
simple looking problems, are sometimes the most challenging ones. --- My Unedited article^
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Quartz... wrote:
Why does a candle extinguishes when we blow on it?
We blow the air away creating a small vacuum pocket and a fire cannot burn in a vacuum. That's my guess anyway :-) Regards, Nish
Nish’s thoughts on MFC, C++/CLI and .NET (my blog)
The Ultimate Grid - The #1 MFC grid out there!I usually clean the wax out of my ears for that effect... Asking someone to define CP is like asking someone to define art. It is a known, a tangable thing, a state of being. To define it is to limit and miss its true nature.
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I want to say this is a nonconverging series, but it's been a long time since I did those in math, and google ignores /'s even when they're inside of quotes.
it's very close to the Harmonic Series[^], it just starts with i=2, instead of i=1. Cleek | Image Toolkits | Thumbnail maker
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I want to say this is a nonconverging series, but it's been a long time since I did those in math, and google ignores /'s even when they're inside of quotes.
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Nishant Sivakumar wrote:
That works on the vacuum principle too, eh?
a wing will create small pockets of (partial) vacuum as air moves around it. it's under debate as to whether this is the actual source of lift or not. Cleek | Image Toolkits | Thumbnail maker
Chris Losinger wrote:
it's under debate as to whether this is the actual source of lift or not.
You mean they still don't know? I've always been told that's why the plane lifts (but honestly, I never quite believed it. Just stick your hand out a moving car window and it seems that the angle of attack has a major affect as well, though maybe that's BECAUSE of the low pressure on the back of one's hand). Marc Pensieve Some people believe what the bible says. Literally. At least [with Wikipedia] you have the chance to correct the wiki -- Jörgen Sigvardsson
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Chris Losinger wrote:
it's under debate as to whether this is the actual source of lift or not.
You mean they still don't know? I've always been told that's why the plane lifts (but honestly, I never quite believed it. Just stick your hand out a moving car window and it seems that the angle of attack has a major affect as well, though maybe that's BECAUSE of the low pressure on the back of one's hand). Marc Pensieve Some people believe what the bible says. Literally. At least [with Wikipedia] you have the chance to correct the wiki -- Jörgen Sigvardsson
Marc Clifton wrote:
You mean they still don't know?
Explains those bumpy rides, and if you are flying Air Canada or a domestic Indian airline, the bumpy part of the ride is seriously stressed upon! Regards, Nish
Nish’s thoughts on MFC, C++/CLI and .NET (my blog)
The Ultimate Grid - The #1 MFC grid out there! -
OK lets divide it in two parts Question 1
Quartz... wrote:
When will the sum of this series exceed 100 ?
Question 2
Quartz... wrote:
Will it EVER ?
simple looking problems, are sometimes the most challenging ones. --- My Unedited article^
Quartz... wrote:
Question 1 Quartz... wrote: When will the sum of this series exceed 100 ?
Don't know. Some very large number, I'm up to around 58000000000 and it's only at about 24.36 doing this by brute force. I'm sure this is some known sequence and there is some very clever and simple way to calculate it, but I'm not up to the challenge.
Quartz... wrote:
Question 2 Quartz... wrote: Will it EVER ?
I'm pretty sure it has to eventually. The number keeps growing but by progressively smaller steps, but it still keeps growing. Shouldn't you ask question 2 first?
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Chris Losinger wrote:
it's under debate as to whether this is the actual source of lift or not.
You mean they still don't know? I've always been told that's why the plane lifts (but honestly, I never quite believed it. Just stick your hand out a moving car window and it seems that the angle of attack has a major affect as well, though maybe that's BECAUSE of the low pressure on the back of one's hand). Marc Pensieve Some people believe what the bible says. Literally. At least [with Wikipedia] you have the chance to correct the wiki -- Jörgen Sigvardsson
Marc Clifton wrote:
You mean they still don't know?
this site[^] explains it pretty well, i think. but it's not the traditioinal Bernoulli's explanation (high pressure below, low pressure above). this one explains it as: The lift of a wing is proportional to the amount of air diverted down times the downward velocity of that air. so, some might know, but the rest of the world disagrees. Cleek | Image Toolkits | Thumbnail maker
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Quartz... wrote:
When will the sum of this series exceed 100 ?
e100? Jon Sagara When I grow up, I'm changing my name to Joe Kickass! My Site | My Blog | My Articles -- modified at 15:12 Tuesday 9th May, 2006
Jon Sagara wrote:
e100?
Wait - after working this a bit, I'm getting that e100 is a good approximation of the number of terms it would take for the sum of that series to get up to 100. Is that what you were indicating? If so, I apologize for my first 'correction' :-O From my musings, the above series is the Harmonic Series, but starting at k=2 (Chris Losinger has noted this already, it appears). In addition, ln(n) is a good approximation of this series' value at n. Therefore solving: ln(n) = 100 for n would approximate the number of terms in the series needed to get the sum of the series to 100. Solving this equation, I get: n = e100 which is what you originally wrote. Did you come to this conclusion in the same way I did? I hope I'm not making myself look silly - I'm 6 years away from my last math class. It's amazing how the details become so fuzzy after such a short time...
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Nishant Sivakumar wrote:
That works on the vacuum principle too, eh?
a wing will create small pockets of (partial) vacuum as air moves around it. it's under debate as to whether this is the actual source of lift or not. Cleek | Image Toolkits | Thumbnail maker
Chris Losinger wrote:
a wing will create small pockets of (partial) vacuum as air moves around it. it's under debate as to whether this is the actual source of lift or not.
Do you have a source for that? I can't think of anything else that would generate lift.
I can imagine the sinking feeling one would have after ordering my book, only to find a laughably ridiculous theory with demented logic once the book arrives - Mark McCutcheon
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Jon Sagara wrote:
e100?
Wait - after working this a bit, I'm getting that e100 is a good approximation of the number of terms it would take for the sum of that series to get up to 100. Is that what you were indicating? If so, I apologize for my first 'correction' :-O From my musings, the above series is the Harmonic Series, but starting at k=2 (Chris Losinger has noted this already, it appears). In addition, ln(n) is a good approximation of this series' value at n. Therefore solving: ln(n) = 100 for n would approximate the number of terms in the series needed to get the sum of the series to 100. Solving this equation, I get: n = e100 which is what you originally wrote. Did you come to this conclusion in the same way I did? I hope I'm not making myself look silly - I'm 6 years away from my last math class. It's amazing how the details become so fuzzy after such a short time...
Russell Morris wrote:
Is that what you were indicating? If so, I apologize for my first 'correction'
Yes. No worries. :) Yeah, that was the same approach I took, but decided, nah, that was too simple, so I crossed it out. I'm about 9 years removed from my last series class, so the details are extremely fuzzy for me, too. Jon Sagara When I grow up, I'm changing my name to Joe Kickass! My Site | My Blog | My Articles
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Troposphere wrote:
The sum will never even reach the number 1, much less exceed 100.
You are kidding, right? :omg: It crosses 1 after the 3rd fraction in the series. 1/2 + 1/3 + 1/4 = 1.08333 Regards, Nish
Nish’s thoughts on MFC, C++/CLI and .NET (my blog)
The Ultimate Grid - The #1 MFC grid out there!Whoops, you're right. I misinterpreted the problem as another age-old math problem. My bad. ø¤º°`°º¤ø,¸¸,ø¤º°`°º¤ø,¸¸,ø¤º°`°º¤ø,¸¸,ø¤º°`°º¤ø,¸¸,ø¤º°`°º¤ø,¸¸,ø¤º°`°º¤ø,¸¸,ø¤º°`°º¤ø,¸
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Quartz... wrote:
Question 1 Quartz... wrote: When will the sum of this series exceed 100 ?
Don't know. Some very large number, I'm up to around 58000000000 and it's only at about 24.36 doing this by brute force. I'm sure this is some known sequence and there is some very clever and simple way to calculate it, but I'm not up to the challenge.
Quartz... wrote:
Question 2 Quartz... wrote: Will it EVER ?
I'm pretty sure it has to eventually. The number keeps growing but by progressively smaller steps, but it still keeps growing. Shouldn't you ask question 2 first?
Wjousts wrote:
I'm sure this is some known sequence and there is some very clever and simple way to calculate it, but I'm not up to the challenge
Actually there is no closed form equation for this series. Brute force is the only way. http://www.shef.ac.uk/pas/SOM104/series.pdf[^]
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Troposphere wrote:
And the candle gets extinguished from the carbon dioxide in our breath.
And if you blow air by some other method it won't ? --- My Unedited article^
Quartz... wrote:
And if you blow air by some other method it won't ?
I did not say that. If you blow air from a fan at high velocity, I'm sure the candle would go out, but you asked why it goes out from us blowing on it, and I think the answer is the carbon dioxide. ø¤º°`°º¤ø,¸¸,ø¤º°`°º¤ø,¸¸,ø¤º°`°º¤ø,¸¸,ø¤º°`°º¤ø,¸¸,ø¤º°`°º¤ø,¸¸,ø¤º°`°º¤ø,¸¸,ø¤º°`°º¤ø,¸
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Marc Clifton wrote:
You mean they still don't know?
this site[^] explains it pretty well, i think. but it's not the traditioinal Bernoulli's explanation (high pressure below, low pressure above). this one explains it as: The lift of a wing is proportional to the amount of air diverted down times the downward velocity of that air. so, some might know, but the rest of the world disagrees. Cleek | Image Toolkits | Thumbnail maker
It definitely makes more intuitive sense then the traditional description. You learn something new every day.
I can imagine the sinking feeling one would have after ordering my book, only to find a laughably ridiculous theory with demented logic once the book arrives - Mark McCutcheon
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Wjousts wrote:
I'm sure this is some known sequence and there is some very clever and simple way to calculate it, but I'm not up to the challenge
Actually there is no closed form equation for this series. Brute force is the only way. http://www.shef.ac.uk/pas/SOM104/series.pdf[^]
Bob Flynn wrote:
Brute force is the only way.
From what I've been reading, ln(n) is a good approximation for the sum of this series computed with n terms. It'll be a bit of considering that the ln(n) approximates the harmonic series, which is the same as this series except for the addition term '1/1'.
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Bob Flynn wrote:
Brute force is the only way.
From what I've been reading, ln(n) is a good approximation for the sum of this series computed with n terms. It'll be a bit of considering that the ln(n) approximates the harmonic series, which is the same as this series except for the addition term '1/1'.
The approximation is good for characterization, but for the answer to the question "when does the series cross 100", an approximation will not provide the correct answer. It could be used to get an idea of how long it will take to do it by brute force - which is recommended because our little CPU's just might not have enough life expectancy to compute the result using brute force.
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The sum will never even reach the number 1, much less exceed 100. And the candle gets extinguished from the carbon dioxide in our breath. Rich ø¤º°`°º¤ø,¸¸,ø¤º°`°º¤ø,¸¸,ø¤º°`°º¤ø,¸¸,ø¤º°`°º¤ø,¸¸,ø¤º°`°º¤ø,¸¸,ø¤º°`°º¤ø,¸¸,ø¤º°`°º¤ø,¸
You're thinking about the "1/2 + 1/4 + 1/8 ..." series. It approaches 1. :)
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1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 ...... When will the sum of this series exceed 100 ? Will it EVER ? For the thinkers, Why does a candle extinguishes when we blow on it? (Never paid attention to it, right?) Looks simple but it isn't ! * you are right, this guy has got nothing to do... but if you read this we are in the same boat --- My Unedited article^
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it's very close to the Harmonic Series[^], it just starts with i=2, instead of i=1. Cleek | Image Toolkits | Thumbnail maker
thanks. I knew I'd seen it. Back of the envelope time to hit 100, give or take an order of magnitude. Needs 200 terms in the orsene sequense. 200th term is a sum of 2^200 terms. 2^200 = 2*((2^10)^10) = 2*(10^3)^10 = 2*10^30 terms. Anyone trying to bruteforce it using floats will fail when sum + 1/n = sum due to precision limits, anyone using a scientific number class with arbitary decimal points will be at it for ~10^13 years assuming 1bn terms/sec.
