Re: New to Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg126400] Re: New to Mathematica*From*: Jaebum Jung <jaebum at wolfram.com>*Date*: Tue, 8 May 2012 04:07:35 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

You could try like the following: r[k_?IntegerQ] := Block[{x}, Max[x /. NSolve[(x/Log[x])*(1 + 1/Log[x]) == 108.2 + k, x, Reals]]] NProduct[1 - 1/r[k], {k, 0, 3000}] ----- Original Message ----- From: "J.Jack.J." <jack.j.jepper at googlemail.com> To: mathgroup at smc.vnet.net Sent: Sunday, May 6, 2012 7:28:55 PM Subject: [mg126400] Re: New to Mathematica Thanks for replying. Responses embedded: On May 6, 8:24 am, Murray Eisenberg <mur... at math.umass.edu> wrote: > First, perhaps folks were reluctant to respond because this looked like > it could be a homework exercise. > > Second, you don't even have proper Mathematica syntax in your equation > relating x and k. Did you even try to read the documentation to learn > the very basics? I tried and tried for hours but couldn't so much as find any section that would even tell me how to write the condition that k be an integer. For example, proper syntax for the equation would be: > > (x/Log[x]) (1 + 1/Log[x]) == 108.2 + k > > Function arguments must be enclosed in brackets, not parentheses, and > the equality is a doubled "=" sign. Moreover, your original expression > had an unbalanced terminal parenthesis. > Thanks. > Third, the equation itself looks really nasty. Aside from the fact that > it mixes exact formulas with an approximate real (108.2), the left-hand > side is transcendental. > > Fourth, the equation does not seem to uniquely define x as a function of > k! For example, form the difference between the two sides... > > f[x_] := (x/Log[x]) (1 + 1/Log[x]) - 108.2 - k > > ... and plot f for, say, k = 2: > > Plot[Evaluate[f[x] /. k -> 2], {x, 0.5, 2}, Exclusions -> {x == = 1}, > AxesOrigin -> {0, 0}, PlotRange -> {-5, 5}] > > The graph crosses the x-axis twice. And indeed, if you use FindRoot with > initial guesses above and below 1, you'll see that this is so: > > FindRoot[Evaluate[f[x] /. k -> 2], {x, 0.9}] > {x -> 0.916554} > > FindRoot[Evaluate[f[x] /. k -> 2], {x, 1.1}] > {x -> 1.11137} > Am sorry, I should have said "let r(k) be the highest x such that..." Can you give me the required inputs? That would help me immensely.