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infinite sum problem


Hi,

the following sum converges only for x<1,
but Mathematica gives a result for general x
when the sum is evaluated symbolically.


In[1]:=
Sum[(-1)^k*x^(2k),{k,0,Infinity}]

Out[1]=
\!\(1\/\(1 + x\^2\)\)

In[2]:=
Sum[(-1)^k*x^(2k),{k,0,Infinity}]/.x\[Rule]2

Out[2]=
\!\(1\/5\)

that's wrong!

In[3]:=
Sum[(-1)^k*2^(2k),{k,0,Infinity}]

correctly gives error: Sum does not converge.


Am I overlooking something?

thanx,
marc


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