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# Homework help, Sequences and Series

Hey guys, I really have a problem with this math/physics exercise.

When dropped, a ball takes 1 second to hit the ground. It then takes 90% of this time to rebound to its new height, and this continues until the ball comes to rest.

the total time of motion is: 1+2(0.9)+2(0.9)^2+2(0.9)^3+...

A) What is the Sn for the series?

B) How long does it take for the ball to come to rest?

Help would be very much appreciated. Tnx.

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What exactly do you need help with?

It's a bit confusing because the first term only looks at the time the ball takes to hit the floor, while the other terms look at how the time it takes to bounce back up, then fall back down (hence the 2 seconds). In this case, you have to model as a=2 and r=0.9, then subtract 1 from the total to account for the first term. Everything else should be fairly straightforward, as you just have to plug it all into the respective formulas for the geometric series.