Thomas Calculus 13th [Solutions]

714 Chapter 10 Infinite Sequences and Series
n
n 10
n
1
27. lim lim 1
1 0
n
diverges
28.
n( n 1) 2
n n 2n
1 2
( 2)( 3) 2
n
n n
n n 5n
6 n
2n
5
n
2
lim lim lim lim 1 0
diverges
29. lim
1
0
n
n
4
test inconclusive
n
n 3
1
2n
30. lim lim 0
2
n
31. lim cos
1
cos0 1 0
n
n
n
test inconclusive
diverges
n n n
e e e
n
n
e n n
n
e 1 n
n
e n
32. lim lim lim lim 1
1 0
1
diverges
33. lim ln
1
0
n
n
diverges
34. lim cos
n
n does not exist diverges
35. s 1 1 1 1 1 1 1 1 1 1 1
k 2 k s
2 3 3 4 k 1 k k k 1 k 1
k k
k 1
1 1 lim lim 1 1,
series converges to 1
3 3 3 3 3 3 3 3 3 3 3
1 4 4 9 9 16 ( k 1) k k ( k 1) ( k 1)
36. sk
3
2 2 2 2 2
3
( k 1)
lim s lim 3 3, series converges to 3
k
k
k
2
37. sk
ln 2 ln 1 ln 3 ln 2 ln 4 ln 3 ln k ln k 1 ln k 1 ln k
ln k 1 ln 1 ln k 1 lim s lim ln k 1 ; series diverges
k
k
k
38. sk
tan1 tan 0 tan 2 tan1 tan 3 tan 2 tan k tan k 1 tan k 1 tan k
tan k 1 tan 0 tan k 1 lim s lim tan k 1 does not exist; series diverges
k
k
k
39.
s k
1 1 1 1 1 1 1 1 1 1 1 1
2 3 3 4 4 5
cos cos cos cos cos cos
1 1 1 1 1 1 1 1 1 1
k k 1 k 1 k 2 3 k 2
cos cos cos cos cos
1 1
3 k 2 3 2 6
lim s k lim cos , series converges to 6
k
k
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