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32m
comment The number of distinct values taken by a sequence of partial sums of iid
@MattSamuel If the $X_i$ are only $0$ or $1$ then $S_i$ is non-negative and weakly increasing so $P(S_1\not =0 , S_2\not =0 , ... , S_n\not =0) =P(S_1\not =0)=P(X_1\not =0) $ which because $X_i$ is i.i.d. is equal to $P(X_n\not =0) = P(\theta_n=\theta_{n-1}+1)$.
41m
comment Is :$\sqrt{i\pi+\sqrt{i\pi+\sqrt{i\pi+\sqrt\cdots}}}$ irrational or transcendental or real number?
With a sensible single-valued definition of $\sqrt{\,\,}$, it converges both when $a=i\pi$ and when $a=\pi$
7h
comment Is :$\sqrt{i\pi+\sqrt{i\pi+\sqrt{i\pi+\sqrt\cdots}}}$ irrational or transcendental or real number?
It is not a real number. Taking the square root to have a positive imaginary part, $1.804133+1.204476i$ is an approximation
7h
comment Is :$\sqrt{i\pi+\sqrt{i\pi+\sqrt{i\pi+\sqrt\cdots}}}$ irrational or transcendental or real number?
If $\sqrt{ }$ is a function, it should only take one value
8h
comment The number of distinct values taken by a sequence of partial sums of iid
I assume the second has a $\forall$ as in is $\displaystyle \lim_{n\rightarrow \infty}\frac{E(\theta_n)}{n}= P(S_k \neq0, \forall k\geq1)$. It should certainly be possible to argue from the first expression that $P(S_k \neq0, \forall k\geq1)$ is a lower bound, and you might be able to go on and say the division by $n$ drives any difference to $0$ in the limit.
8h
answered The number of distinct values taken by a sequence of partial sums of iid
8h
comment Numbers written into a square grid
Interesting that a natural layout (e.g. left to right, higher rows first) has no difference greater than $n+1$
8h
answered Numbers written into a square grid
10h
comment Strategy for choosing lottery numbers when buying many tickets
What you are looking for is a lottery wheel. Since $10000\times {5 \choose 4}/{50 \choose 4} \approx 0.2$, while $10000\times {5 \choose 3}/{50 \choose 3} \approx 5.1$, and $10000\times {5 \choose 2}/{50 \choose 2} \approx 81.6$, I would have thought that a sensible priority might be to avoid choosing sets of five which avoid having $4$ or $5$ elements in common with other sets and which minimise the number of cases of having $3$ in common with other sets.
13h
comment What is the value of the expression: $(1+\frac 12)(1+\frac 13)(1+\frac 14)…(1+\frac {1}{2004})(1+\frac {1}{2005})$?
Essentially the same as Mark Bennet's hint
13h
comment What is the value of the expression: $(1+\frac 12)(1+\frac 13)(1+\frac 14)…(1+\frac {1}{2004})(1+\frac {1}{2005})$?
Essentially the same as Mark Bennet's hint
19h
awarded  Enlightened
19h
comment expected number of steps for chossing randomly each number between 1 to $n$ at least $k$ times
According to Wikipedia, Donald J. Newman and Lawrence Shepp found $ n \log n + (k-1) n \log\log n + O(n)$ in the "The double dixie cup problem"
20h
awarded  Nice Answer
20h
comment Probability of drawing >18 when drawing 3 cards
Drawing with or without replacement? Do Aces and picture cards count $0$ in the sum or do you draw again? With a computer it would be easy enough to consider every equal probable draw. You could alternatively use a generating function approach though I doubt it would make the calculations easy.
20h
revised Optimal Control question (Economics)
image
1d
comment Taking the square root of an imaginary number
Given a non-zero imaginary or complex number $z$, there are two complex numbers with $w^2=z$
1d
comment Combinations and Double Factorials
Child marriages?
1d
revised If $x_{n+1}\leq x_n + 1/n^2$ then $x_n$ converges
added 161 characters in body
1d
answered If $x_{n+1}\leq x_n + 1/n^2$ then $x_n$ converges