The input


produces output


which is correct for $|d|<1$. But for $|d|\geq1$ the sum does not converge so the output is wrong.

Why does Mathematica not produce any warning or indication that this is the case?

For more complicated cases where the non-convergence might not be obvious upon cursory inspection, is there a way for Mathematica to output both a sum and a condition for convergence?

  • 3
    $\begingroup$ You can check first with SumConvergence, SumConvergence[d^t, t] gives Abs[d] < 1 $\endgroup$
    – Jason B.
    Commented Mar 11, 2016 at 9:55

1 Answer 1

Sum[d^t, {t, 0, Infinity}, GenerateConditions -> True]

ConditionalExpression[1/(1 - d), Abs[d] < 1]


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