Another Silly puzzle

Jon Sagara

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

Richard Andrew x64

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,¸

Bob Flynn

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[^]

Richard Andrew x64

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,¸

Andy Brummer

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

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[^]

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]

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.

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