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6

It's not a bug and it's not so uncommon. For an explanation have a look here. This and some related issues also appear in this MathGroup thread. Also relevant: 1 2.


3

They are not identical computations. With the first form, (mu/2 gt).gt Mathematica can take advantage of vector arithmetic, usually going through specialized routines like LAPACK. The second form, Sum[(mu[[i]]/2 gt[[i]]) gt[[i]], {i, Length@mu}] however, will usually be calculated term by term because there is a possibility that the input can change ...


2

If I understand your question, there is no need of Mathematica to solve your problem for $x_0$ given, we know that $y_{n+1} = y_{n} + 5$. We know also that $y_0 y_1 = 12500$. That is to say that $y_0 y_1 = y_0 (y_0 + 5) = y_0^2 + 5 y_0 = 12500$. You can ask Mathematica to solve this second order equation to obtain $x_0 = 109.331$ --- there is also a ...



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