E1: Reset to a = 0.5
The partial sum series converges to 2.
How does the sequence evolve?
Try mentally to explain to a child how summing infinite finite numbers, none of which has a zero value, can lead to a finite value!
E2: Choose a around + 1
Obviously convergence of the partial sums needs a < 1.
What is the condition for the members of the sequence?
E3: Choose a < 1.
Compare sequence and series.
E4: Observe the red point in the limit window and compare with the series charts.
E4: Imagine: a = 0.5 . Now 10, 1000, 1000000 members of another sequence with increasing member value, whose respective sum is 50, 1000000, 1012 is added to the geometric series. Will the total sum be convergent? If yes, what is its limit?
E5: Which range of the index decides if an arbitrary series with finite members is convergent or not?