Math Is Fun Forum

for nothing.

Nope.
It would be cool if it was.
I have it as a kind of present. It helps me much for some problems.
But there exist many free math programs - I've had a link somewhere - and some of them are even better than mathematica in some cases.

Or more general:

Yep. But maths helps better, because we know:

double sum(double x, int n){
return (pow(x,n+1)-1)/(x-1)
}
(and more efficient, too)

No I haven't.
this doesn't depend of n. Using Pingenhole proncipe, my sum ends with b+1 balls, because it's thoughtless to go further.
I used something like this - I'm cuonting all the possible combinatins with k balls and computing the probability to make a combination of k balls, multyplying them, and summazing for all k form 2 balls to b+1 balls. This gives me the aritmetic mean of the wheighted elements in the list, so the expected number of balls. It's tricky to understand, that the probability to get a combination with mare balls is less than the probability to get a combination with less balls.
And, as you can see from the picture above, the formula works!

Nope. We're sure only for 7/s^t.
So 7^2/(s^t)^2 = s^2t, option 1

Sorry for the ten posts.
Now - a little break

I founded it at least!
I had to leave my original function, because the omega function became so complicated.
I used another approach, which is hard to explain, and now I have a formula, which agrees with the experimental results:
First, I defined a function, S:

I like it this way:

It basically means that if √2 is a rational, than there exist integers a,b, (a,b)=1, such that a^2=2b^2, so 2/a^2, but 2 is prime, so 4/a^2. But then 2/b^2, so 2/b, and we ,have 2/a and 2/b ,so (a,b)>=2, which is contradiction.

In my opinion the intuition and the knowledge are the most important.
If you don't have intuition, it will be hard to develop alone.
If you don't have knowledges, you'll waste your time end intuition on subjects, already discovered, instead of learning them.

Or, it just isn't a question:

It doesn't end with question mark