How to correctly evaluate limits with parameters

Questions
,
1

Limit[(t^2 (-1 + t^k))/(-1 + t), k → +Infinity] //
FullSimplify[#, 0 < t < 1] &

The code is not correctly calculating the right limit value, where the parameter t ranges from 0 < t < 1. The correct result should be t²/(1 - t). How can this be obtained?

2

Try passing the assumptions to Limit[]:

Limit[(t^2 (-1 + t^k))/(-1 + t), k -> +Infinity, 
 Assumptions -> 0 < t < 1]