[CAS] limit() question

[DrD]

I encountered this limit example:

limit(ABS((x-2)^(n+1)/((n+1)^2*3^(n+1)) / ((x-2)^n/(n^2*3^n))),n,∞); ==> undef

During a simplification process, (of the underlying expression), a result is obtained at this equivalent expression:

limit(ABS((x-2)*n^2/((n+1)^2*3)),n,∞); ==> ABS(x-2)/3

Further simplification continues to return ABS(x-2)/3. Should the original (un-simplified) expression, also return this result, (instead of "undef")?

-Dale-

[parisse]

Yes, undef is expected, because limit does series expansion without simplifications (because simplify could return a much harder limit), and you can not do that for (x-2)^n without assumption on x (need to know the sign of ln(x-2)). If you run for example assume(x>3) the initial limit will be solved. Or if you run simplify, because it will remove the (x-2)^n.

[DrD]

Thank you for your explanation, Parisse.

-Dale-