This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 /...
View
Full
Document
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.
 Fall '07
 Hohnhold
 Calculus

Click to edit the document details