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# infinte series problem!!

Posted 9 years ago
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Posted 9 years ago
 Dear Kevin,sorry I do not understand what you mean. Could you explain that again?Best wishes,Marco
Posted 9 years ago
 hi ,this is my friend's question and i have no more information ,sorr.....!!
Posted 9 years ago
 i want to Similarity solution
Posted 9 years ago
 Hi,That series does not converge. Sum[Cos[2 i x], {i, 1, Infinity}] gives Sum::div: Sum does not converge. >> Cheers,M.
Posted 9 years ago
 One could do a little better In:= Clear[q, o, x] {#, If[q = Sum[Cos[2 o x], {o, 1, \[Infinity]}, Regularization -> #]; Head[q] === Sum, "Divergent", q]} & /@ {"Abel", "Borel", "Cesaro", "Dirichlet", "Euler"} Out= {{"Abel", "Divergent"}, {"Borel", 1/2 (-Cos[2 x] - 2 Sin[x]^2)}, {"Cesaro", "Divergent"}, {"Dirichlet", -(1/2)}, {"Euler", "Divergent"}} see the abcd[e] of divergent series. It's interesting that Cesaro's regularization is divergent in general, but In:= Sum[Cos[2 o 1/2], {o, 1, \[Infinity]}, Regularization -> "Cesaro"] Out= -(1/2) Abel holds also a special value (the alternating sum of 1) In:= Sum[Cos[2 o \[Pi]/4], {o, 1, \[Infinity]}, Regularization -> "Abel"] Out= -(1/2) Is it clear that there is no 0 < x < Pi for which the conventional sum exists? This is also an input In:= Sum[Cos[2 o x], {o, 1, \[Infinity]}, VerifyConvergence -> False] Out= -(1/2) with other words, Dirichlet.
Posted 9 years ago
 hi, can you plot it, i want to look ,thanks you!!
Posted 9 years ago
 can you plot it Follwing the movie Mr. and Ms.Smith may I ask you to define it? What would you like the see plotted?