I need to conduct this massive calculation of factorials but apparently my phone can't do it. I need to confirm whether the result is lesser or greater than 10^85.
Is there any way I could do this calculation without the use of a supercomputer?
Help me out bros
>Is there any way I could do this calculation without the use of a supercomputer?
Yes.
No.
96160064 - 94657563 = 1502501
hope that helps
This.
The expression in the pic can be simplified to
[eqn] {94657563 choose 1502501}[/eqn]
We have many formulas to bound binomial coeffiecients.
https://en.wikipedia.org/wiki/Binomial_coefficient#Bounds_and_asymptotic_formulas
Either way this is far far larger 10^85.
the most you will need is 85 people with 10 fingers each maybe try to recruit a team the mall
What if I did this weird 10 finger thing 85 times myself?
you will shoot your load all the way to the ceiling and it will drip back upon your body while you sleep like the wax of icarus
i don't give a frick about the ! operator
>I need to confirm whether the result is lesser or greater than 10^85.
it's about [math]10^{3361186} gg 10^{85}[/math]
Your formula is reducible to, approximately,
[math] frac{10^9!}{10^7! (10^9 - 10^7)!} [/math]
If we use Stirling's approximation, we find an explicit lower bound, approximately:
[math]frac{(10^9)^{10^7}}{(10^7)^{10^7}} = 10^{10^7} gg 10^{85} [/math]
greater
Well since 96160064-94657563 is 1502501, that means that 96160064!/94657563! is the first 1502501 terms of 96160064! multiplied together (and the 1502501! in the denominator is pretty negligible here it's so small in comparison). The first eleven terms alone of 96160064! are going to be greater than 10^85 and we don't only have eleven terms.. we have over a million terms. So yeah, this number is going to be frickhuge, much much bigger than you could write down on a piece of paper even if that piece of paper is as big as the whole world.
As for why the 1502501! in the denominator is negligible.. it has an equal amount of terms being multiplied together as our numerator does (after factoring out the 9465765! from numerator and denominator). Same amount of terms but the numerator's terms are in the range of 94657563 through 96160064 whereas the denominator's are in the range of 1 through 1502501. When multiplying every number 94657563 through 96160064 together that is so huge you won't even notice multiplying all numbers 1 through 1502501 together
btw I am using logic here, not anything I learned in a math book or a math class. Frick school, school is dumb. Use logic and read textbooks to get smart at math.
oki found the answer am i allowed to help him?
ok well i'm not going to give the ans without encouragement, but without formulas, just with 6 very straightforward steps you can prove a lower bound of 2109^751250.
Well here is proof of a lower bound: the lower bound is 2109 because if you multiply more than one 2109 together they are going to be bigger than 2109 since 2109>1
what do I win? gay
show work
My post lays out every detail, illiterate fricktard. n*n>n if and only if n>1, are you seriously too fricking dumb to grasp that fact?
2109^n > 2^n * 10^3n
2^10n > 10^3n
2109^n > 10^.3n * 10^3n
2109^n > 10^3.3n
2109^751250 > 10^2479125
what do I win homosexual
Ai generated math is just the worst
2109=10^y
log2109=ylog10
log2109/log10=y
y=log(2109)
2109=10^log(2109)
2109^751250=(10^log(2109))^751250
2109^751250~10^2497212.530529289
10^2497212.530529289>10^2497212.530529288
so 10^2497212.530529288 is a lower bound
and 10^2497212.530529290 is an upper bound
did I show enough work for you moron?
oh wait I thought you were saying that you want to prove the lowr bound of 2109^751250 rather than that 2109^751250 is the lower bound of something else so feel free to disregard
and
and
and please use proper english next time so we do not run into this misunderstanding again 🙂
say "lower bound as being" instead of "lower bound of"! 🙂
"lower bound for the value of the expression in the post asking if the value of an expression is more or less than 10^85"
No I mean I could point out that any approximation while convincing is not a proof unless you also prove the bounds on the error of the estimation (of the value of the expression in the post asking if the value of an expression is more or less than 10^85).
But beyond my preference for using a bound, my solution is actually very very simple, so I think it might be just right for OP, unless he was supposed to learn Sterlings approximation.
Then post it homosexual, or don't, but stop being a homosexual "hey guys I have this solution but I'm not gonna post it yet lol!"
Jesus ok let let me finish this cig and i'll go take a photo.
whoops it was actually 2209^75125
Jesus, 2209^751250.
Correct orientation:
Wtf why is it sideways. Anyway.
Why do you care Black person I do everything sideways
https://www.wolframalpha.com/input?i=factorial+96160064+%2F+factorial+94657563+%2F+factorial+502501
Stirling's approximation