Calculus Early Transcendentals 2nd Edition by William L Briggs http://testbankair.com/download/solutions-manual-for-calculusearly-transcendentals-2nd-edition-briggs-by-william-l-briggs Link full download test bank: Link full download Solutions Manual: http://testbankair.com/download/solutions-manual-forcalculus-early-transcendentals-2nd-edition-by-william-l-briggs 8.1 An Overview 8.1.1 A sequence is an ordered list of numbers a1 , a2, a3 , , often written {a1 , a2 , } or { an } For example, the natural numbers {1, 2, 3, } are a sequence where an = n for every n 8.1.2 a1 = = 1; a2 = ; a3 = ; a4 = ; a5 = 8.1.3 a1 = (given); a2 = · a1 = 1; a3 = · a2 = 2; a4 = · a3 = 6; a5 = · a4 = 24 8.1.4 A finite sum is the sum of a finite number of items, for example the sum of a finite number of terms of a sequence P 8.1.5 An infinite series is an infinite sum of numbers Thus if { a n } is a sequence, then a + a2 + · · · = ∞ ak k= P , then ∞k = ak = P ∞k = k is an infinite series is an infinite series For example, if ak = k 8.1.6 S1 = P k = 1; S2 = k =1 P k =1 P k = + = 3; S3 = k =1 k = + + = 6; S4 = P k =1 k = + + + = 10 8.1.7 S1 = P P k =1 k = 1; S2 = k =1 k = + = 5; S = P k =1 k = + + = 14; S = P k =1 k = + + + 16 = 30 .1 1 + P S1 = k =1 k = + + 14= 12 8.1.9 a = ; a2 = 10 = 1; S2 = P k = 1k = ; S3 = 1+ 2= P k = 1k = 1+ 2+ 3= ; S4 = P k = 1k = 1 ; a3 = ; a4 = 10000 100 1000 8.1.10 a = 3(1) + = a2 = 3(2) + = 7, a3 = 3(3) + = 10, a = 3(4) + = 13 8.1.11 a1 = − , a2 = = 21 a3 = − = − 13 , a4 = = 8.1.12 a = − = a = + = 3, a3 = − = 1, a4 = + = 8.1.13 a = 2+ 1 = a2 = 22 + 1 = a3 = +1 8.1.14 a1 = + = 2; a2 = + = ; a3 = + = 10 = a4 = ; a4 = + = 24 + 17 = 17 8.1.15 a1 = 1+ si n(π /2) = 2; a2 = 1+ si n(2π /2) = + si n π = 1; a = 1+ si n(3π /2) = 0; a4 = 1+ si n(4π /2) = + sin 2π = 2 2 8.1.16 a1 = · − · + = 0; a2 = ·2 − · + = 3; a3 = · − · + = 10; a4 = · − · + = 21 Chapter Sequences and Infinite Series 8.1.17 a1 = 2, a2 = · = 4, a3 = 2(4) = 8, a4 = · = 16 8.1.18 a1 = 32, a2 = 32/2 = 16, a3 = 16/2 = 8, a4 = /2 = 8.1.19 a1 = 10 (given); a2 = · a1 − 12 = 30 − 12 = 18; a3 = · a2 − 12 = 54 − 12 = 42; a4 = · a3 − 12 = 126 − 12 = 114 8.1.20 a1 = (given); a2 = a1 − = 0; a3 = a2 − = −1; a4 = a3 − = 8.1.21 a1 = (given); a2 = · a1 + + = 2; a3 = · a2 + + = 15; a4 = · a3 + + = 679 8.1.22 a0 = (given); a1 = (given); a2 = a1 + a0 = 2; a3 = a2 + a1 = 3; a4 = a3 + a2 = 8.1.23 8.1.24 a 32 , 64 a −6 , b a1 = 1; an + = n b a = 1; a n + = (−1 ) c an = n− c an = (−1 ) 8.1.25 n+1 n (|an | + 1) n 8.1.26 a −5 , a 14, 17 b a1 = −5 , an + = −an b a1 = 2; an + = an + n c an = (−1 ) · c an = −1 + 3n 8.1.27 8.1.28 a 32, 64 a 36, 49 b a1 = 1; an + = 2an √ b a1 = 1; an + = ( an + 1) c an = 2n−1 c an = n 8.1.30 8.1.29 a 243, 729 a 2, b a1 = 1; an + = 3an b a1 = 64; an + = n c an = 3n−1 c an = n−1 = 27− n 8.1.31 a1 = 9, a2 = 99, a3 = 999, a4 = 9999 This sequence diverges, because the terms get larger without bound 8.1.32 a1 = 2, a2 = 17, a3 = 82, a4 = 257 This sequence diverges, because the terms get larger without bound 8.1.33 a1 = 10 , a2 = 100 , a3 = 1000 , a4 = 10,000 This sequence converges to zero 8.1.34 a1 = 10 , a2 = 100 , a3 = 1000 , a4 = 10,000 This sequence converges to zero 1 1 8.1.35 a1 = − , a2 = , a3 = − , a4 = This sequence converges to because each term is smaller in absolute value than the preceding term and they get arbitraril y close to zero 8.1.36 a1 = 0.9, a2 = 0.99, a3 = 0.999, a4 = 9999 This sequence converges to Copyright 2c015 Pearson Education, Inc Thank you for using www.freepdfconvert.com service! Only two pages are converted Please Sign Up to convert all pages https://www.freepdfconvert.com/membership ... , a4 = This sequence converges to because each term is smaller in absolute value than the preceding term and they get arbitraril y close to zero 8.1.36 a1 = 0.9, a2 = 0.99, a3 = 0.999, a4 = 9999... Copyright 2c015 Pearson Education, Inc Thank you for using www.freepdfconvert.com service! Only two pages are converted Please Sign Up to convert all pages https://www.freepdfconvert.com/membership... sequence diverges, because the terms get larger without bound 8.1.32 a1 = 2, a2 = 17, a3 = 82, a4 = 257 This sequence diverges, because the terms get larger without bound 8.1.33 a1 = 10 , a2