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6h
comment Closed-form of infinite continued fraction involving factorials
not too far from $459/314$
7h
comment How to find fast modular exponentiation?
$n^{5^4}\equiv 1 \pmod{11251}$
7h
comment How to find fast modular exponentiation?
It is not too difficult to find $5448^5 \pmod{11251}$, then do that again, and again
1d
comment Does alternating test show divergence?
If $a_n$ has a non-zero limit then the alternating series sum will certainly not converge to a finite number
1d
comment Inverse of $f(x)= x+\sin(x)$?
You are unlikely to be able to achieve much more than a series expansion which might start $\dfrac12 y + \dfrac1{96} y^3 +\dfrac{1}{1920} y^5+\cdots$
1d
comment Combinations - no repetition for mirrors?
Are you asking why $1+4$ could be seen as distinct from $4+1$ but $4+4$ is seen as the same as $4+4$?
1d
answered Give an example of a function who is nondifferentiable on (0, 2) but has an antiderivative on (0, 2)
1d
comment Obtaining the Poisson distribution in the calculator.
@Michael Hardy: about $0.999167$ of the actual value, so not bad. You could still need logarithms.
1d
answered Obtaining the Poisson distribution in the calculator.
2d
comment Find the nth in geometric progression
$2,10,50,\ldots$
2d
comment Prove inequalities with induction
A more interesting question might be showing the sum is between $\sqrt{n}$ and $2\sqrt{n}$
2d
comment Prove inequalities with induction
But $\dfrac{1}{\sqrt{1}}+\dfrac{1}{\sqrt{2}}+\dfrac{1}{\sqrt{3}} \gt 2 \gt 2-\dfrac2n$ for all positive $n$
2d
comment How to get the maximum and minimum number of length $m$ and the sum of the digits $s$
+1 and to have any solution, the sum of the digits must be at least $1$ and no more than $9$ times the number of digits.
2d
comment Does this algorithm find prime numbers only?
Most modern definitions do not treat $1$ as a prime number
2d
comment Prove inequalities with induction
It might be easier to look at $P(1),P(2),P(3)$ and then wonder whether there is an error in the question
2d
answered What is the best choice given a probability and a cost for each choice?
2d
comment What distribution would describe this?
@GenericNickname: Indeed the probability of any one basket being good is ${90 \choose 10}/{100 \choose 10}\approx 0.33$ so the expected number of good baskets is about $3.3$
2d
comment What distribution would describe this?
For a large numbers of eggs, the form of a reasonable approximation depends on whether you have a large number of baskets or a small number of baskets.
2d
comment Probability that n people collectively occupy all 365 birthdays
Since you have to subtract your expression from $1$, I would have $\displaystyle \sum_{m=0}^{365} (-1)^{m}{365 \choose m} \left(1 - \dfrac{m}{365}\right)^n$ as the answer to the original question.
2d
comment The vertical projection of a chord of a circle?
The heights above the horizontal diagonals of the two points are $R\cos(t_o)$ and $R\cos(t_i)$, perhaps easier to see if you join them to the centre, perpendicularly to the tangents. It gives the same result as your expression when $t_o=0$, i.e. horizontal though you call this "$90$ degrees with respect to the vertical"