Thomas Calculus 13th [Solutions]

CHAPTER 10
INFINITE SEQUENCES AND SERIES
10.1 SEQUENCES
1. a 1 1
1 0, 1 2 1
2 2 ,
2
1
2 4
1 3 2
3
3 9
1 4 3
4
4 16
a a , a
2
2
2. a 1
1 1, 1 1
1!
a 2 2! 2 , a 1 1
3 3! 6 , a 1 1
4 4! 24
3.
2
( 1)
a1 2 1
1,
a ( 1) 3
1 a 4
5
( 1) 1
2 4 1 3 ,
3 6 1 5 ,
( 1)
a 1
4 8 1 7
4.
1
a 1 2 ( 1) 1,
2
a 2 2 ( 1) 3,
3
a 3 2 ( 1) 1,
4
a 4 2 ( 1) 3
5. a 2 1
1 ,
2
2 2
a
2
2 1
2 3 2
2
,
a
3
2 1
3 4 2
2
,
a
4
2 1
4 5 2
2
6. 2 1 1
1 2 2 ,
2 1 3
2 ,
2 4
a
2
a
2
a
3
2 1 7
3 3 8
2
,
a
4
2 1 15
4 4 16
2
7. a 1 1, 1 3
2 1 ,
2 2
3 1 7
3 2 2 4
7 1 15
4 4 2 8
a a , a ,
2
3
4
a 511
9 256 , a 1023 10 512
a 15 1 31
5 , 63
8 2 16
a 6 32 , a 127
7 64 , a 255
8 128 ,
8. a1 1, 1
2 2 ,
1
1
1
a a 2 1 a 6 1
24 1
3 3 6 ,
a 1
9 362,880 , a 1 10 3,628,800
4 4 24 ,
a 5 5 120 , a 1
6 720 , a 1
7 5040 , a 1
8 40,320 ,
2
( 1) (2)
9. a1 2, a2 1,
( 1) 3
(1) 1
2 3 2 2 ,
a 1
8 64 , a 1
9 128 , a 1 10 256
4 1
5 a a ( 1)
( 1)
1
2 1
4
4 2 4 ,
a 1
5 2 8 , a 1
6 16 , a 1
7 32 ,
1 ( 2)
2 ( 1)
10. a1 2, a2 1,
2
2
3 3 3 ,
a 1
8 4 , a 2
9 9 , a 1 10 5
2
a a 3
4
1
3 1
2
4 4 2 ,
a 2
5 5 5 , a 1
6 3 , a 2
7 7 ,
11. a1 1, a2 1, a3 1 1 2, a4 2 1 3, a5 3 2 5, a6 8, a7 13, a8 21, a9 34, a10 55
12. a1 2, a2 1, 1
3 2 ,
1
1
a a 2 1
2
4 1 2 ,
a5 1, a6 2, a7 2, a8 1, a 1
9 2 , a 1 10 2
1
2
13.
n 1
n
an
( 1) , n 1, 2,
14. an
( 1) , n 1, 2,
15.
n 1 2
an
( 1) n , n 1, 2,
16.
n 1
( 1)
an
, n 1, 2,
2
n
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