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infinte series problem!!

Posted 10 years ago


cos(2x)+cos(4x)+cos(6x)+cos(8x) infinte

i do this for a long time but in vain and i am tired so i po it here. can anyone help me!! how to solve this problem!!

POSTED BY: kevin kevin
7 Replies

Dear Kevin,

sorry I do not understand what you mean. Could you explain that again?

Best wishes,


POSTED BY: Marco Thiel
Posted 10 years ago

hi ,this is my friend's question and i have no more information ,sorr.....!!

POSTED BY: kevin kevin
Posted 10 years ago

i want to Similarity solution

POSTED BY: kevin kevin


That series does not converge.

Sum[Cos[2 i x], {i, 1, Infinity}]


Sum::div: Sum does not converge. >>



POSTED BY: Marco Thiel

One could do a little better

In[36]:= 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[37]= {{"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[38]:= Sum[Cos[2 o 1/2], {o, 1, \[Infinity]}, Regularization -> "Cesaro"]
Out[38]= -(1/2)

Abel holds also a special value (the alternating sum of 1)

In[43]:= Sum[Cos[2 o \[Pi]/4], {o, 1, \[Infinity]}, Regularization -> "Abel"]
Out[43]= -(1/2)

Is it clear that there is no 0 < x < Pi for which the conventional sum exists? This is also an input

In[47]:= Sum[Cos[2 o x], {o, 1, \[Infinity]}, VerifyConvergence -> False] 
Out[47]= -(1/2)

with other words, Dirichlet.

POSTED BY: Udo Krause
Posted 10 years ago

hi, can you plot it, i want to look ,thanks you!!

POSTED BY: kevin kevin

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?

POSTED BY: Udo Krause
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