# Summing infinite series that converge only for some parameter values

The input

Sum[d^t,{t,0,Infinity}]


produces output

1/(1-d)


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?

• You can check first with SumConvergence, SumConvergence[d^t, t] gives Abs[d] < 1 – Jason B. Mar 11 '16 at 9:55

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