Another Silly puzzle

[Andy Brummer]

It definitely makes more intuitive sense then the traditional description. You learn something new every day.

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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

[Russell Morris]

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'.

[Bob Flynn]

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.

[Jorgen Sigvardsson]

You're thinking about the "1/2 + 1/4 + 1/8 ..." series. It approaches 1. :)

[Bob Flynn]

is it 20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000?

[Dan Neely]

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.

[Somanova420]

Wow, I like read that exact same page off a Google search.:laugh:

[Russell Morris]

Somanova420 wrote:

Wow, I like read that exact same page off a Google search

I spent the first 20 minutes poking through Wolfram's mathweb stuff, trying to decide what type of series it was. It wasn't until I stumbled upon the Wikipedia page for series that it listed this series as the harmonic series, along with approximations. I got a solid A on this stuff in CalcIII back in college - now I'm looking at it through what seems to be foggy, frosted glass only a handful of years later :-O -- Russell Morris Morbo: "WINDMILLS DO NOT WORK THAT WAY!"

[Phil J Pearson]

Chris Losinger wrote:

(partial) vacuum

My Physics teacher would have ranted at you! "Vacuum is a total absence of air. How can you have a partial total absence? You mean 'a pocket of lower air pressure'" Phil

[Maxwell Chen]

http://www.math.com/tables/expansion/power2.htm[^]

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Maxwell Chen

[Maxwell Chen]

Summation applet[^]. 1) Click the [Applet] button, a popup window is seen. 2) Input 1/(n+1), 3) Click [Auto] button. :-D [Edit] Ouch! Overflow ... ;P [/Edit]

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Maxwell Chen

[Chris Losinger]

Phil J Pearson wrote:

My Physics teacher would have ranted at you!

i would've ranted back. ;) Cleek | Image Toolkits | Thumbnail maker

[Bob Flynn]

That's not the answer to the question.

[Maxwell Chen]

Bob Flynn wrote:

That's not the answer to the question.

It is! See the 1st raw in the table.

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Maxwell Chen

[Bob Flynn]

Yes, I saw it. It said that the sum goes to infinity as n goes to infinity. But the question was when does the sum reach 100? If ever. You definitely got the "if ever part", but that left the much more difficult problem of what is the value of n when the sum equals 100.

[Dan Neely]

I order of magnituded the eta for 100 here. Unless there's an analytical method getting a precise value is impossible since bruteforce isn't an option. http://www.codeproject.com/script/comments/forums.asp?msg=1480757&forumid=1159#xx1480757xx

[Bob X]

Nishant Sivakumar wrote:

We blow the air away creating a small vacuum pocket and a fire cannot burn in a vacuum. That's my guess anyway

Sorry. You cannot blow into an area and create a vacumm caused by no matter in an area. This is physically impossible through the laws of physics. Carbon Dioxide doesn't put out the flame either because your breath contains a large amount of oxygen in it. If I remember correctly, the flame goes out due to over supplying oxygen to the flame. Similar to why an airplane engine will stall if you make the fuel too rich.

[Raj Lal]

The real solution is here [^] --- My Unedited article^