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Unformatted text preview: n th time and write it in a closed form (ie, not an inﬁnite sum). Solution: The total vertical distance travelled when the ball hits the ﬂoor for the n th time is 15 + 2( 2 3 )(15) + 2( 2 3 ) 2 (15) + 2( 2 3 ) 3 (15) + · · · + 2( 2 3 ) ( n1) (15) . Notice that 15 + ( 2 3 )(15) + ( 2 3 ) 2 (15) + ( 2 3 ) 3 (15) + · · · + ( 2 3 ) ( n1) (15) is a ﬁnite geometric series with n terms, a = 15 and x = 2 3 and so sums to 15(1( 2 3 ) n ) 12 3 = 45(1( 2 3 ) n ) . The total distance can then be expressed in closed form as 2 ± 45(1( 2 3 ) n ) ²15 = 90 ± (1( 2 3 ) n ) ²15 . Page 2...
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This note was uploaded on 11/07/2010 for the course MATH 10C math 10c taught by Professor Rosanna during the Spring '10 term at UCSD.
 Spring '10
 rosanna

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