HW2 even solutions

HW2 even solutions - Homework 2 Solutions 9.2.6 No Ratio between successive terms is not constant 2 x 2 x = 2 x while 3 x 3 2 x 2 = 3 2 x 9.2.8 Yes

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Unformatted text preview: Homework 2 Solutions 9.2.6 No. Ratio between successive terms is not constant: 2 x 2 x = 2 x , while 3 x 3 2 x 2 = 3 2 x . 9.2.8 Yes, a = y 2 , ratio of successive terms is y . 9.2.16 The series has 10 terms. The first term is a = 0 . 2 and the constant ratio is x = 0 . 1 , so Sum = . 2(1- x 10 ) (1- x ) = . 2(1- (0 . 1) 10 ) . 9 = 0 . 222 . 9.2.18- 2 + 1- 1 2 + 1 4- 1 8 + 1 16- ··· = ∞ X n =0 (- 2)- 1 2 n , a geometric series. Let a =- 2 and x =- 1 / 2 . Then ∞ X n =0 (- 2)- 1 2 n = a 1- x =- 2 1- (- 1 / 2) =- 4 3 . 9.2.20 Using the formula for the sum of a finite geometric series, 20 X n =4 1 3 n = 1 3 4 + 1 3 5 + ··· + 1 3 20 = 1 3 4 1 + 1 3 + 1 3 2 + ··· + 1 3 16 ! = (1 / 3) 4 (1- (1 / 3) 17 ) 1- (1 / 3) = 3 17- 1 2 · 3 20 . 9.2.29 (b) The first drop from 10 feet takes (1 / 4) √ 10 seconds. The first full bounce (to 10 · (3 / 4) feet) takes (1 / 4) p 10 · (3 / 4) seconds to rise, therefore the same time to come down. Thus, the full bounce, up and down, takes 2(1 /...
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This homework help was uploaded on 04/11/2008 for the course MATH 10C taught by Professor Hohnhold during the Fall '07 term at UCSD.

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HW2 even solutions - Homework 2 Solutions 9.2.6 No Ratio between successive terms is not constant 2 x 2 x = 2 x while 3 x 3 2 x 2 = 3 2 x 9.2.8 Yes

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