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Evaluating the Sum

Sum[a^i, {i, ∞}]

yields

-(a/(-1 + a))

which obviously only holds true for $\left|a\right|<1$. Why doesn't Mathematica give a limitation for the validity of the solution?

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    $\begingroup$ Sum[a^i, {i, ∞}, GenerateConditions -> True] will return the necessary conditions. $\endgroup$ – J. M. is away Jul 27 '16 at 8:09
  • $\begingroup$ @J.M. OK, thanks. It seems as if I have to get used to MMA thinking more than I do ;) $\endgroup$ – DPF Jul 27 '16 at 8:18
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    $\begingroup$ It seems a conspicuous inconsistency to me that Sum has GenerateConditions->False by default , while Integrate has it True ( eg Integrate[a^i, {i, 1, Infinity}] ). $\endgroup$ – george2079 Jul 27 '16 at 20:40
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Thanks to @J. M. this solution gives the answer:

Sum[a^i, {i, ∞}, GenerateConditions -> True]

It returns a ConditionalExpression, in the above case:

ConditionalExpression[-(a/(-1 + a)), Abs[a] < 1]
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    $\begingroup$ In addition: look at SumConvergence[a^i, i]. $\endgroup$ – J. M. is away Jul 27 '16 at 11:29

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