Jaime
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 Dec 28 comment geometric series with probability The sum of the digits of your student number is 11, and its largest digit is 1, so you should actually solve it for k=9. Dec 19 comment Minimizing a functional definite integral Look up calculus of variations (en.wikipedia.org/wiki/Calculus_of_variations), to see how these type of problems are normally dealt with. In your case, as Vibert points out, either $f(g)=0$ or $f(g) = -\inf$, depending on how you define minimisation, is the solution to your problem. Dec 11 comment What is the necessary condition for a matrix to have eigenvalue 1? There must be a vector that is unchanged by multiplication with the matrix, I don't really think there is much more to it... Dec 7 comment Improving Newton's iteration where the derivative is near zero? You could approximate your function at $x$ by a parabola, using $f(x)$, $f'(x)$ and $f''(x)$, instead of a line using just the first two... Dec 7 comment Counting strings with given numbers of occurrences of 0 and 1, and containing a given substring Figuring out the sequences with two, but not more, consecutive 1s is the difficult thing... Dec 7 comment Counting strings with given numbers of occurrences of 0 and 1, and containing a given substring Ok, so it's not the same, but if instead of 3 consecutive 1s you are after only 2 consecutive 1s, the formula for "in how many ways can you arrange m 1s in n positions without having two consecutive 1s" is Binomial[n-m, m]. So you will have at least two consecutive ones in Binomial[n,m] - Binomial[n-m,m]. Figuring out how many have two, but not three consecutive 1's is beyond me right now... Dec 7 comment Counting strings with given numbers of occurrences of 0 and 1, and containing a given substring I thought about that one, but then you are counting 1 (111) ... and (111) 1 ... as different, which they are not. Your formula doesn't produce the right result for his first example Oct 2 comment How to complete the argument to find the solution of the following non-linear O. D. E.? Methinks you are missing a $'$ in the RHS of your original equation (*)