P^2+Σ2P

We are back to civilized society, but this is heads or tails. This is gambling like stock market . The average line is 50%, so you have two choices which are up or down. 1 is head. 0 is tail. P is probability. If you have a die, probability of 1 is 1/6. P(X=1)=1/6 0 is the other. ∴ P(X=0)=5/6 You have dice 10 times, and you get one 6 times. P(X=6)=10C6*(1/6)^6*(5/6)^(10-6)≒0.2170635% This is how many times you have 1 in 10 times. dice -

Orientalism is no formula. It is often mysticism of numbers. We can see algorism, but nobody knows where it comes from. Chinese blocks such as 一、二、三 are well known. Constructors gather and pile them. You still see their temples. Wood is vanishing ironically. Polynomial keeps expanding, but there is a pattern. You keep adding numbers infinitely. We often see it naturally in the modern age. x+y=1C0*x^0*y+1C1*x*y^0=x+y (x+y)^2=2C0*x^0*y^2+2C1*x*y+2C2*x^2*y^0=x^2+2xy+y^2 (x+y)^3=3C0*x^0*y^3+3C1*x*y^2+3C2*x^2*y+3C3*x^3*y^0=x^3+3x*y^2+3x^2*y+y^3 (x+y)^4=4C0*x^0*y^4+4C1*x*y^3+4C2*x^2*y^2+4C3*x^3*y+4C4*x^4*y^0=x^4+4x*y^3+6x^2*y^2+4x^3*y+y^4 1 1 1 2 1 1 3 3 1 1 4 6 4 1 We know that this is convergence .

I am a Japanese , so I am interested in mysterious something. AI still don't understand our consciousness. Future is uncertain, so you may change it. I am not so curious about it. It is hard to read this Chinese character, but I try to translate it. B0 B0*2C0 B0*3C0+B1*3C1 B0*4C0+B1*4C1+B2*4C2 B0*5C0+B1*5C1+B2*5C2+B3*5C3 B0*6C0+B1*6C1+B2*6C2+B3*6C3+B4*6C4 B0*7C0+B1*7C1+B2*7C2+B3*7C3+B4*7C4+B5*7C5 1 1 3 1 4 6 1 5 10 10 1 6 15 20 15 1 7 21 35 35 21 B0 B1 B2 B3 B4 B5 B0=1, B1=-1/2 but 1/2, B2=1/6, B3=0, B4=-1/30, B5=0 Now I see Bernoulli numbers in the Samurai era, although the country has been closed except for Holland and Portugal . We never know it in those days. Some Europeans may have taught us. B6=1/42. I clearly see it. We don't understand the reason, but it seems to be Pascal's triangle. N=6 and K=4 5C3=10 Then this samurai multiplies Bernou...

Bernoulli numbers are almost the sum of k power. Bn is the Bernoulli number. This is recurrence relation, so you change the direction back and forth. You can also write this. This is Maclaurin's expansion . Then you can see this. f(x)*(1/f(x))=1 This is convergence. ∴ from (2) This is Binomial Coefficient. ∴ EX. B0=1 B1=-1/2*(2C0)*B0=(-1/2)*1*1=-1/2 B2=-1/3*(3C0*B0+3C1B1)=(-1/3)*(-1/2)=1/6 B3=-1/4*(4C0*B0+4C1*B1+4C2*B2)=-1/4*(1-2+1)=0 B4=-1/5*(5C0*B0+5C1*B1+5C2*B2+5C3*B3)=(-1/5)*(1/6)=-1/30 All Bernoulli number is rational . Bn is related to Riemann zeta function . n→∞