Which geometric series converges?

0.02+0.02+0.02+0.02+...

4+0.08 +0.0016+0.000032+

4+80+ 1.600+ 32,000+.

0.02+0.04+0.08+0.16+.

4+0.08 +0.0016+0.000032+

Step-by-step explanation:

a+ar+ar²+ar³+ar⁴+…

the  geometric series converges if  |r| < 1

The geometric series converges:

4+0.08 +0.0016+0.000032+

0.08=4*0.02

0.0016=4*(0.02)²

0.000032=4*(0.02)³

r=0.02<1

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.