I am looking at the expansion of a time series Series [$\left(\sum_{s=1}^\infty\frac{r}{(1+k)^s}x^{s+1}\right)^{-1}${x, 0, 2} and I get a result like

1 + (r x^2)/(1 + k) + SeriesData[x, 0, {}, 0, 3, 1]

If I now simplify the above term first, I get $\frac{1}{1-\frac{x^2 r}{1+k-x}}$. Running the Series-command on the invers of this term, i.e., Series[1-(x^2 r)/(1 + k - x) gives me a different answer then the one above. This seems to be a bug or am I making a mistake here? enter image description here


You write "Running the Series-command on the inverse of this term ..." but that term is already the inverse you want to run the Series-command on.

enter image description here


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