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Masalah Sama dari Carian Web
sum of all coprimes of a number.
https://math.stackexchange.com/questions/569210/sum-of-all-coprimes-of-a-number
Yes, the formula is right and if you reached it by yourself it is remarkable. If \;\phi(n)\; is Euler's Totient Function, then the sum you want is \frac n2\phi(n)=\frac{n^2}2\prod_{p\mid n\,,\,p\,\text{a prime}}\left(1-\frac1p\right) ...
How much money should we take?
https://math.stackexchange.com/questions/459602/how-much-money-should-we-take
Let f(n) be the expected final win for a player already having a balance of n and employing the optimal strategy. Trivially, f(n)\ge n as he might decide to stop right now. However, if the ...
P(A \cap B) = \frac14, P(\neg A) = \frac13, P(B) = \frac12, P(A \cup B) =?
https://math.stackexchange.com/questions/2003363/pa-cap-b-frac14-p-neg-a-frac13-pb-frac12-pa-cup-b
You correctly state that: P(A\cup B) = P(A)+P(B)-P(A\cap B) Then you try to calculate P(A\cap B) from P(A) and P(B) when (a) you do not know that they are independent and (b) you already ...
Calculating the fair price of an option knowing that selling the stock to the market carries a 2\% fee
https://math.stackexchange.com/questions/2268663/calculating-the-fair-price-of-an-option-knowing-that-selling-the-stock-to-the-ma
The solution for this would be Risk Neutral Probability = \frac{(1-d-(1+r)k)}{u-d-(1+r)k} Fair Price of the Option = \frac{1}{1+r}\left(p\psi{(u)}+(1-p)\psi{(d)}\right) where \psi{(u)} = Max((110-100),0) = 10 ...
Prove that \frac{1}{a(a-b)(a-c)} +\frac{1}{b(b-c)(b-a)} +\frac{1}{c(c-a)(c-b)} =\frac{1}{abc} for all sets of distinct nonzero numbers a,b,c.
https://math.stackexchange.com/questions/1579934/prove-that-frac1aa-ba-c-frac1bb-cb-a-frac1cc-ac-b
First, I'll mention an elementary way to finish the proof. Observe that this could be done by expanding the following product: f(c)=bc(b−c)−ac(a−c)+ab(a−b)−(a−b)(a−c)(b−c). At the end, you ...
What sort of particles corresponds to the (1,1/2) representation of the Lorentz group?
https://physics.stackexchange.com/q/439085
I think that my question wasn't actually well defined. For starters, when you restrict to the SO(3) subgroup of the (j_1, j_2) rep. of the Lorentz group, you get the j_1 \otimes j_2 rep of ...
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3 \frac{ 3 }{ 7 }
4 \frac{ 15 }{ 32 }
1 \frac{ 1 }{ 2 } +3 \frac{ 4 }{ 5 }
1 \frac{ 1 }{ 2 } -3 \frac{ 4 }{ 5 }
1 \frac{ 1 }{ 2 } \times 3 \frac{ 4 }{ 5 }
1 \frac{ 1 }{ 2 } \div 3 \frac{ 4 }{ 5 }
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