Solutions manual for calculus early transcendentals 2nd edition by william l briggs

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.. 8.1.5 An infinite series is an infinite sum of numbers... absolute

k = 1

1

Calculus Early Transcendentals 2nd Edition by William L Briggs

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8.1.2 a1 = 1 = 1; a2 = 2 ; a3 = 3 ; a4 = 4 ; a5 = 5

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

8.1.5 An infinite series is an infinite sum of numbers Thus if { a n } is a sequence, then a1 + a2 + · · · = P ∞ ak

k =

is an infinite series

1 + 2 + 3 + 4 = 10

1 + 4 + 9 + 16 = 30

1

; a2 = 10

1

1

1

8.1.11 a1 = − 1 , a2 = 1 = 1 a3 = − 2 = − 1 , a4 = 1 = 1

8.1.13 a1 = 2+ 1 = 3 a2 = 22 + 1 = 5 a3 = 23 +1 = 9 a4 = 24 + 1 = 17

8.1.14 a1 = 1 + 1 = 2; a2 = 2 + 1 = 5 ; a3 = 3 + 1 = 10 ; a4 = 4 + 1 = 17

1 + sin 2π = 1.

P

1 + 1 + + 1 = 2

k =1 k

1 2 3 4 12

=

k

2

126 − 12 = 114.

8.1.23

a 32 , 64

b a1 = 1; a n + 1 = n

8.1.24

a −6 , 7.

(|a n | + 1).

8.1.25

a −5 , 5.

b a1 = −5 , a n + 1 = −a n

c a n = (−1 ) n · 5.

8.1.27

a 32, 64

b a1 = 1; a n + 1 = 2a n

c a n = 2n−1

8.1.29

a 243, 729

b a1 = 1; a n + 1 = 3a n

8.1.26

a 14, 17

b a1 = 2; a n + 1 = a n + 3

8.1.28

a 36, 49

b a1 = 1; a n + 1 = (√

an + 1)2

c a n = n2

8.1.30

a 2, 1

b a1 = 64; a n + 1 = n

n = = 27− n

bound

bound

absolute value than the preceding term and they get arbitraril y close to zero

Copyright 2c015 Pearson Education, Inc

n − 1

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