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Oct
12
comment Question about generating function
What makes you think that there is a closed form? What do you know about hypergeometric functions?
Oct
12
answered Tricky proof: sum of adjacent integers
Oct
12
answered Proving the number of permutations $A,B\;$ with $n+1$ total cycles and $AB=(123\cdots n)$ is $C_n$
Oct
12
comment How do I evaluate the Complex Integral $(z^{-n})/(e^z−1) $ using residue theory?
@Peter What is "the usual" way to calculate Bernoulli numbers?
Oct
12
comment How do I evaluate the Complex Integral $(z^{-n})/(e^z−1) $ using residue theory?
@Peter You misunderstand my point. There is no simple closed formula for the Bernoulli numbers, so you have to say what you want. Asymptotics? Recurrence? Double sum? You find all this in the wikipedia article on Bernoulli numbers.
Oct
12
answered Matrix multiplication: is C(AB) the same as (CA)B?
Oct
12
comment Can I use my powers for good?
You could give advice to people in debt or tutor students from bad high schools. But I guess that you forgot to mention what your minimum requirements are for salary and lack of boredom.
Oct
12
answered How do I evaluate the Complex Integral $(z^{-n})/(e^z−1) $ using residue theory?
Oct
11
comment When does $a + b$ divide $a^p + b^p$?
If the gcd of a and b is not 1 or p, then the statement is obviously wrong.
Oct
11
answered Why does $a^n - b^n$ never divide $a^n + b^n$?
Oct
11
answered When does $a + b$ divide $a^p + b^p$?
Oct
11
comment Mathematical explanation behind a picture posted (lifted from facebook)
I think that this would make a fine question for the proposal area51.stackexchange.com/proposals/4955/popular-natural-science so I invite you to support the proposal.
Oct
11
comment How to solve such an equation ? (Line-Plane Intersection)
What do you mean with "solve"? Do you want to calculate $t$? Do you know the relation between the V and the x, y, z?
Oct
10
comment How to compute the limit of this integral?
For large n and x smaller than 1- epsilon, $x^n$ is small, for small argument, the function is near $f(0)$.
Oct
10
comment Simplifying a series
It is a geometric series.
Oct
10
answered How to compute the limit of this integral?
Oct
10
comment What's the lower bound of the sum $S(n) = \sum_{k=1}^n \prod_{j=1}^k(1-\frac j n)$?
Is $i=k$ ? (not enough characters)
Oct
10
comment Marble game theory
@Brian M.Scott Note that the IMO problem has two parts. The first part is about emptying just one of the three accounts which is exactly equivalent to making two accounts the same size.
Oct
9
comment Marble game theory
Positive is also not always advisable as there are languages/countries where 0 is positive and negative.
Oct
9
revised Marble game theory
added 411 characters in body