9.1 Sequences and Series by SGLee - HSKim -SWSun
1-3. Find a formula for the general term 
of the sequence, assuming that the pattern of the first few terms continues.
1. 
.
Therefore, 
.
Calculus-Sec-9-1-Solution
9.1 Sequences and Series by SGLee - HSKim -SWSun
1-3. Find a formula for the general term of the sequence, assuming that the pattern of the first few terms continues.
1.
.
Therefore, .
2. 
.
Therefore, 
.
3. 
Therefore, 
.
4-15. Determine whether the sequence converges of diverges. If it converges, find the limit.
4. 
http://matrix.skku.ac.kr/cal-lab/cal-10-1-4.html
11. 
Here, 
and 
.
Thus, 
.
Hence, this series is divergent.
12. 
Thus, 
Hence, this series is divergent.
13. 
Hence, this series is divergent.
14. 
By L'Hopital's Rule,
Hence, this series is convergent.
15. 
Since 
,
Therefore, 
Hence, this series is convergent.
16. Investigate the sequence 
defined by the recurrence relation 
for 
.
In particular, show that 
.
Therefore, 
17. Let 
.
(a) Determine whether 
is convergent.
(b) Determine whether 
is convergent.
(a)
Therefore, 
is convergent.
(b)
Therefore, 
is divergent.
18-24. Determine whether the following series is convergent or divergent. Find the sum if it is convergent.
18. 
Thus, 
is divergent.
19. 
http://matrix.skku.ac.kr/cal-lab/cal-10-1-19.html
This is a geometric series and since 
, this series is convergent.
And, 
.
20. 
But, 
is not convergent and 
is convergent.
Thus, 
is divergent.
21. 
.
Therefore, 
is convergent to 
.
22. 
By L'Hopital's Rule,
Therefore, 
is divergent.
23. 
Since 
, this geometric series with 
(
) is convergent.
And, 
.
24. 
As 
, 
Thus, 
is divergent.
25-26. Express the number as a ratio of integers.
25. 
5. 
6. 
7. 
8. 
9. 
10. 
.
