infinity vs finite

If you have a finite number of tasks to be done in a finite amount of time, can it be done? Simple arithmetic question

If you have a finite number of tasks to be done in an infinite amount of time, can it be done? trivial

If you have an infinite number of tasks to be done in a finite amount of time, can it be done? Needs some math analysis on convergence vs divergence
Example: 1 + 1/2 + 1/4 +...=2, which means in can be done under this frame.
Proof: Assume series on LHS converges to X
So X-1=1/2 + 1/4 + 1/6=0.5X
therefore X-1=0.5X
=> X=2

If you have an infinite amount of tasks to be done in an infinite amount of time, can it be done? Needs logical arguments, but arguments for both sides have been produced and recoginzed.

Morale of story: There exist infinities of different cardinality, in fact there exist an infinite amount of infinities.