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**Heldensheld****Member**- Registered: 2006-07-01
- Posts: 25

SEQUENCE AND SERIES

Geometric series

A ball takes 1 second to hit the ground when dropped. It then takes 90% of this time to rebound to its new height and this continues unil the ball comes to rest.

a) Show that the total time of motion is given by 1 + 2(0.9) + 2(0.0)^2 + 2(0.9)^3 + .....

b) Find Sn for the series in a.

c) How long does it take for the ball to come to rest.

Please show how you came to the conclusions....ty.

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,319

Sn-0.9Sn= 1+ 2(0.9) -0.9 + 2(0.9)^2-2(0.9)^2 +...+2(0.9)^(n-1) -2(0.9)^(n-1)-2(0.9)^n

=1+0.9+0+...-2(0.9)^n

So Sn=10(1.9-2(0.9)^n)

n->smaller and smaller

Sn shall be no larger than 10(1.9)=19 as far as I am concerned.

The standard answer to this problem might be 19, meaning 2(0.9)^n has come to 0 as n has reached infinity.

**X'(y-Xβ)=0**

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,685

a) The first fall takes 1 second, the time rising and falling will be the same hence 2(0.9) for the next rise and fall. Each time around is 90% of the previous, so the next time is 90% of 90%, the next is 90% of 90% of 90%, etc, hence:

1 + 2(0.9) + 2(0.9)^2 + 2(0.9)^3 + ...

George has the rest of the answer

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**Heldensheld****Member**- Registered: 2006-07-01
- Posts: 25

Thanks guys...I'll look at it when I'm back from camp.

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