How to sum infinite series?

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After an unsuccessful month attempting to get Axiom to sum an elemental
infinite series, I am joining my first newsgroup to ask if Axiom is able to
do it. Here are some ways I have found not to get the correct result:

(3) -> sum(x**n/n, n=1..%plusInfinity)
   There are 6 exposed and 2 unexposed library operations named sum
      having 2 argument(s) but none was determined to be applicable.
      Use HyperDoc Browse, or issue
                               )display op sum
      to learn more about the available operations. Perhaps
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named sum
      with argument type(s)
                             Expression(Integer)
                 SegmentBinding(OrderedCompletion(Integer))
      Perhaps you should use @ to indicate the required return type, or
      $ to specify which version of the function you need.
(3) -> limit(sum(x**n/n, n=1..k), k=%plusInfinity)

   (3)  "failed"
                                                    Type:
Union("failed",...)
(4) ->

Of the open source CAS I've tried, only Sympy has been able to sum this
infinite series. I am using Mathematica and Maple out of desperation. If I
want to prove the correctness of their results, I can't, because their
methods are trade secrets.

Thank you

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<div dir=3D"ltr">After an unsuccessful month attempting to get Axiom to sum=
 an elemental infinite series, I am joining my first newsgroup to ask if Ax=
iom is able to do it. Here are some ways I have found not to get the correc=
t result:<div><br></div><div><div>(3) -&gt; sum(x**n/n, n=3D1..%plusInfinit=
y)</div><div>=C2=A0 =C2=A0There are 6 exposed and 2 unexposed library opera=
tions named sum=C2=A0</div><div>=C2=A0 =C2=A0 =C2=A0 having 2 argument(s) b=
ut none was determined to be applicable.=C2=A0</div><div>=C2=A0 =C2=A0 =C2=
=A0 Use HyperDoc Browse, or issue</div><div>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0)display op sum</div><div>=C2=A0 =C2=A0 =C2=A0 to learn more about th=
e available operations. Perhaps=C2=A0</div><div>=C2=A0 =C2=A0 =C2=A0 packag=
e-calling the operation or using coercions on the arguments</div><div>=C2=
=A0 =C2=A0 =C2=A0 will allow you to apply the operation.</div><div>=C2=A0</=
div><div>=C2=A0 =C2=A0Cannot find a definition or applicable library operat=
ion named sum=C2=A0</div><div>=C2=A0 =C2=A0 =C2=A0 with argument type(s)</d=
iv><div>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Expression(Integer)</div><div>=C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0SegmentBinding(Order=
edCompletion(Integer))</div><div>=C2=A0 =C2=A0 =C2=A0 Perhaps you should us=
e @ to indicate the required return type, or</div><div>=C2=A0 =C2=A0 =C2=A0=
 $ to specify which version of the function you need.</div><div>(3) -&gt; l=
imit(sum(x**n/n, n=3D1..k), k=3D%plusInfinity)</div><div><br></div><div>=C2=
=A0 =C2=A0(3)=C2=A0 &quot;failed&quot;</div><div>=C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 Type: Union(&quot;failed&quot;,...)</div><div>(4) -&gt;=C2=A0</d=
iv></div><div><br></div><div>Of the open source CAS I&#39;ve tried, only Sy=
mpy has been able to sum this infinite series. I am using Mathematica and M=
aple out of desperation. If I want to prove the correctness of their result=
s, I can&#39;t, because their methods are trade secrets.</div><div><br></di=
v><div>Thank you</div><div><br></div><div><br></div></div>

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