Daniel Krenn
  • Member for 11 years, 5 months
  • Last seen more than a month ago
Math puzzles for dinner
7 votes

There is a plane with 100 seats and we have 100 passengers entering the plane one after the other. The first one cannot find his ticket, so chooses a random (uniformly) seat. All the other passengers ...

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Does $\frac{\mbox{lcm}(1,2,\dots,n+1)}{\mbox{lcm}(1,2,\dots,n)}\to\infty$?
Accepted answer
4 votes

The answer is "no", the limit does not exist, because (now I'm just collecting the comments already made...) consider the series $(2p_n-1)_n$, where $p_1,p_2,\dots$ denote all primes. We have $$\...

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Approximating a recursively-defined function
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3 votes

Rewriting the recursion yields $$1 = \sum\limits_{1\leq i \leq k} \frac{i\ f(i)}{k+i-1}.$$ By assuming $f(k)=\frac{1}{k \ln 2} (1+o(1))$ --- where the little o-Notation $o(1)$ simply means that it is ...

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Uncountable Sets
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2 votes

Assume the interval $[0,1)$ is countable. Then we can write down all numbers like that: $a_0 = 0.a_{0,0}a_{0,1}a_{0,2}\dots$ $a_1 = 0.a_{1,0}a_{1,1}a_{1,2}\dots$ $a_2 = 0.a_{2,0}a_{2,1}a_{2,2}\dots$ $...

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