teh solution for this one is e

but before theinvention/discovery/creation of e

no one could have figured it out

what are the possibilities taht this infinite series is like the one shown above

that there really is no rational answer taht we can put in fractional form?]]>

actually, why doesn't 1/n converge? because 1/n gets smaller and smaller towards 0, i would have thought it would converge?

That's a good question and I wish I had a sufficient answer. Basically, it just doesn't converge fast enough. But I still find series like this mysterious.

]]>5 0.1781080031080031

10 0.17861794090836494

15 0.1787163312115937

20 0.17875125640305384

25 0.1787675393766264

30 0.17877642383782857

35 0.17878179703796668

40 0.17878529205149957

45 0.17878769217497648

50 0.17878941118940814

55 0.1787906843899262

60 0.17879165359266566

65 0.1787924084010432

70 0.17879300768311585

75 0.17879349140653122

80 0.17879388747893882

85 0.17879421586516644

90 0.17879449115322782

95 0.17879472420280887

after 140,000 iterations: 0.17879676889075347

after 1,000,000 iterations: 0.17879676889075347

after 100,000,000 iterations: 0.17879676889075347

pretty safe to say it converges.

----

actually, why doesn't 1/n converge? because 1/n gets smaller and smaller towards 0, i would have thought it would converge?

]]>shocamefromebay, no trust me, it DOES converge, you program is wrong:

this doesnt necessarily mean that its wrong

it just means that it has reached the point where it converged yet

Mathsyperson rewrote it as an alternating series, which is fine. But an alternating series can only have its terms reordered if it is absolutely convergent. This one isn't.

]]>I'm not sure if that helps any, but it would be nice to find an exact answer if we can.

]]>simple AS2 script:

var s:Number = 0;

var i:Number = 1;

function onEnterFrame():Void

{

for(var j:Number = 0; j<5000; j++)

{

s+= 1/(3*i*(3*i-1)*(3*i-2));

i++;

}

trace(i+" : "+s);

}

printing a value every 5000 times, you get to:

140001 : 0.178796768890753

from which point it doesn't change

]]>i made a prog on my calc about 5 mins ago to do sequences for me

and usually if the number converges

it jsut rounds and give me that number that it converges to

and i put this one into it

and it just kept increasing

for like 45 mins

then i just turned it off

and the calc couldnt even turn the number into fractions form

so i think if its byond the power of my calcy

its beyond the power of me

but this shows that this problem

is pretty difficult]]>

Edit: Heh, post collision and we say almost exactly the same thing. Weird.

I wouldn't say weird. 1/n^2 is a very popular series and the original series is 1 / something*something else*something else. It only makes sense to compare this to 1/n^2.

]]>Each term in that sum is smaller than the equivalent term in

, but that sum is finite.Edit: Heh, post collision and we say almost exactly the same thing. Weird.

]]>what are the possiblities that this does not get infinitly close to one number

and just constantly increases?

None. It can be easily shown that each term is less than 1/n^2, and the sum of 1/n^2 converges. Thus, this must converge.

So we may say:

The rest is just algebra.

]]>