Well...I'm interested in the stimulation of growth of plants...especially if there are any studies about pulsed lasers at low frequency ( 5Hz-20KHz ), with wavelengths that stimulate photosynthesis ...the wavelength doesn't matter too much...I just want pulsed lasers that stimulate plants to...
It seems I was wrong...at least I tried...
And you just let me say all these foolish things ? Without putting forward any valid argument ?
(I still have to check my statements...)
My apologies...
Let's take x=p/q; p,q - integers; q<>0;
For n=2q we have n!x=(2q-1)!*2q*p/q=(2q-1)!*2p which is an even number...so...for n large enough the product is an even number of pi's...
I didn't say that was a number less then one...it's a sequence (or whatever it's called)...it's not fixed...n still...
The only problem is that you don't know how "less than one" the cosine is...it's not a "fixed" number...
And...why should be there 2m ? (the cosine can't be -1 for n large enough...n!x -> even)
The best thing is that you reduced it to irrational numbers...
That's what I think of your...
Ok...you are both right...
but i believe you are still wrong about the problem...
about taking those limits separately...
And what kind of medication is there for my condition ?
HallsofIvy...I did not attack your person...but a statement...so...please...at least the idea I was trying to...
That argument will never be an integer multiple of pi...maybe it will come close enough to it...so that sin->0...anyway...I don't think the limits should be taken separately...not first lim m and then lim n...but at the same time...
I don't know if this helps anyone so I'll stop here...:)...
What tends to infinity ?
I know sin*sin is between 0 and 1...but for the argument n!*pi*x i hope it (sin*sin) tends to 0...
something like n!*pi*x tends to an even multiple of pi for n great enough...so that sin*sin -> 0...that's maybe why it's 2*m...not only m...
Here's an idea...
cos(n!*pi*x)^(2*m)=[cos(n!*pi*x)^2]^m=[1-sin(n!*pi*x)^2]^m...
if only one could prove that sin(n!*pi*x)^2 -> 0 as n -> infinity...it would be quite simple from here...it's "classical" (1-1/u)^u where u->infinity...
? did help ?
Sorry to disturb...but nothing happens to a number between -1 and 1 raised to higher and higher powers...think of e=(1-1/n)^n...(sorry i can't help anymore...)
Aaaa...and for that probability problem...the first on the 3rd page...with x and y pennies...
P(x)=x/(x+y)...P(x)->the probability that the player with x pennies wins...
P(y)=y/(x+y)...P(y)->...
Proof ? Somesort of recursivity...too long to be written here...
Are you sure that c is incorrect ?
Remember:the baloon is attached to the floor...not to a weight that floats in the air and is attached to the floor by a string...soooo...why should c be incorrect ?
If it was attached to a weight than it should move forward...
And why do you think that the...