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 Aug 19 awarded Commentator Aug 19 comment Create a C++ program to evaluate the following series: $\sin x \approx x - \frac{x^3}{3! }+\frac{x^5}{5!}-\frac{x^7}{7!}\cdots\pm\frac{x^n}{n!}$ You'd change it to \approx because the series is approximating sin(x), not evaluating it exactly. Aug 19 answered Create a C++ program to evaluate the following series: $\sin x \approx x - \frac{x^3}{3! }+\frac{x^5}{5!}-\frac{x^7}{7!}\cdots\pm\frac{x^n}{n!}$ Aug 18 accepted Random Walk Expected Number of Visits Aug 18 comment Random Walk Expected Number of Visits Ah okay, that makes sense. Thanks for your help! Aug 18 comment Random Walk Expected Number of Visits So if it were the case that both A and E were destination states, the answer to the question: Suppose a walker starts in vertex C. What is the expected number of visits to B before the walker reaches A? would come from the same matrix as the question: Suppose a walker starts in vertex C. What is the expected number of visits to B before the walker reaches E? Aug 18 comment Random Walk Expected Number of Visits First, you are absolutely right about the minus signs. I somehow convinced myself that $$0 - \frac{1}{3} = \frac{1}{3}.$$ And to be clear, that (C, B)th entry of the matrix M accounts for the fact that our destination is vertex A, right? And that would be because we designated A as an absorbing state? Aug 18 asked Random Walk Expected Number of Visits Aug 13 comment Invariant Probability Vector Yep, that's exactly what I know how to do. You've been very helpful; thanks again! Aug 13 awarded Student Aug 12 awarded Scholar Aug 12 comment Invariant Probability Vector The first part of your response makes sense, but before reading this book I'd never heard the term left eigenvector. I took Linear Algebra a year ago so I can find the eigenvalue, but I couldn't tell you how to find the left eigenvector. Aug 12 comment Invariant Probability Vector Ahh this makes so much more sense now. Thank you! Aug 12 accepted Invariant Probability Vector Aug 12 asked Invariant Probability Vector Jul 30 awarded Supporter Jul 27 comment hints on solving $\sin^2 x {d^2y \over dx^2} = 2 y$ Another way to come by what @PeterTamaroff got is by using double angle formulas. $$cos(2x) + 1 = 2cos^2(x)$$ $$sin(2x) = 2sin(x)cos(x)$$ Substituting these in will yield the correct answer. Jul 24 awarded Teacher Jul 24 answered Possible distance b/w points Jul 20 comment Survival function Are you looking for the median or the mean?