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Mathematic Methods HW Solutions 1

# Mathematic Methods HW Solutions 1 - I = i ∞ a n dn ρ =...

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Chapter 1 1.1 (2 / 3) 10 = 0 . 0173 yd; 6(2 / 3) 10 = 0 . 104 yd (compared to a total of 5 yd) 1.3 5/9 1.4 9/11 1.5 7/12 1.6 11/18 1.7 5/27 1.8 25/36 1.9 6/7 1.10 15/26 1.11 19/28 1.13 \$1646.99 1.15 Blank area = 1 1.16 At x = 1: 1 / (1 + r ); at x = 0: r/ (1 + r ); maximum escape at x = 0 is 1 / 2. 2.1 1 2.2 1/2 2.3 0 2.4 2.5 0 2.6 2.7 e 2 2.8 0 2.9 1 4.1 a n = 1 / 2 n 0; S n = 1 - 1 / 2 n 1; R n = 1 / 2 n 0 4.2 a n = 1 / 5 n - 1 0; S n = (5 / 4)(1 - 1 / 5 n ) 5 / 4; R n = 1 / (4 · 5 n - 1 ) 0 4.3 a n = ( - 1 / 2) n - 1 0; S n = (2 / 3)[1 - ( - 1 / 2) n ] 2 / 3; R n = (2 / 3)( - 1 / 2) n 0 4.4 a n = 1 / 3 n 0; S n = (1 / 2)(1 - 1 / 3 n ) 1 / 2; R n = 1 / (2 · 3 n ) 0 4.5 a n = (3 / 4) n - 1 0; S n = 4[1 - (3 / 4) n ] 4; R n = 4(3 / 4) n 0 4.6 a n = 1 n ( n + 1) 0; S n = 1 - 1 n + 1 1; R n = 1 n + 1 0 4.7 a n = ( - 1) n +1 parenleftbigg 1 n + 1 n + 1 parenrightbigg 0 ; S n = 1 + ( - 1) n +1 n + 1 1; R n = ( - 1) n n + 1 0 5.1 D 5.2 Test further 5.3 Test further 5.4 D 5.5 D 5.6 Test further 5.7 Test further 5.8 Test further 5.9 D 5.10 D 6.5 (a) D 6.5 (b) D Note: In the following answers,
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Unformatted text preview: I = i ∞ a n dn ; ρ = test ratio. 6.7 D, I = ∞ 6.8 D, I = ∞ 6.9 C, I = 0 6.10 C, I = π/ 6 6.11 C, I = 0 6.12 C, I = 0 6.13 D, I = ∞ 6.14 D, I = ∞ 6.18 D, ρ = 2 6.19 C, ρ = 3 / 4 6.20 C, ρ = 0 6.21 D, ρ = 5 / 4 6.22 C, ρ = 0 6.23 D, ρ = ∞ 6.24 D, ρ = 9 / 8 6.25 C, ρ = 0 6.26 C, ρ = ( e/ 3) 3 6.27 D, ρ = 100 6.28 C, ρ = 4 / 27 6.29 D, ρ = 2 6.31 D, cf. ∑ n-1 6.32 D, cf. ∑ n-1 6.33 C, cf. ∑ 2-n 6.34 C, cf. ∑ n-2 6.35 C, cf. ∑ n-2 6.36 D, cf. ∑ n-1 / 2 1...
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