Handout 10 Practice for Series Tests .pdf

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Practice Problems for Series

Cal II (Fall 2017)

Determine whether the following series is convergent or divergent. For series that are not
with positive terms, determine if they are absolute convergent or conditional convergent.
1.


X
n=1

5.


X

2n
2
n +1

2.

π n 31−n

6.

n=1

9.


X
n=2

13.

1
n(ln n)2


X
n=2


X
n+1
n=1


X
22n
3n−1
n=1

10.


X
ln n
n=2



n+1
n−1

n!

14.

n


X
n=1

1
n1+1/n



X
n
18.
2n + 3
n=1

 n

X
2
n
21.
3
n=1

22.

25

n=1

29.

4n


X
n100 100n
n=1

n!


X
n!
33.
99n
n=1

37.


X
n=1

41.


X
n=1

26.


X
n!
100n
n=1

X
3 − cos n
2

n=1

30.

n3 − 2

2

X
2n

n=1

7.


X
(−1)n
n2 − 1
n=1

X
n=1

11.

15.

19.

n!



n+1−
n

 
1
12.
n sin
n
n=1


n−1

2n


X
(−2)n−1

n+1
n=1


X
n!
27.
nn
n=1

X

20.


X
(3n + 1)n

n3n

39..

−n2

ne

24.

43.


X
n=1

47.

1
n + 2n

1
1.5 + cos 2n


X
(−1)n−1 (n − 1)
n=1

1 of 1


X
n=1

32.


X
n=1


X
n=1


X
(−1)n

en

n=1

n=1


X
cos 2n
42.
1 + 2n
n=1

n=1


X
n2 − 5n
. 16.
n3 + n + 1
n=1

10n
(n + 1)42n+1

n
∞  2
X
n +1
28.
2n2 + 1
n=1

2n
∞ 

X
X
1
(2n)!
34.
1+
35.
n
(n!)2
n=1
n=1

46.


X
(−1)n
√ .
n
n=1

X


X
n cos(nπ)




X
(−1)n (ln n)

45.
n
n=2

8.

ln n


X


X

( n2 + n − n)
n=1

1
n+1

n=1

23.

4.


X
(−1)n

n=1

31.

X 5n
1
38.
n + n cos2 n
3n + 4n
n=1
3n n!
(n + 3)!


4

n=2


X
n+2
17.
(n + 1)3
n=1


X
sin 4n

3.

3n + 1

36.


X
n=1

40.


X
n=1

48.

n3 + 1
3n2 + 4n + 2

ln

n
3n + 1




X
1 · 3 · 5 · · · · · (2n − 1)
n=1

44.



2 · 5 · 8 · · · · · (3n − 1)
4n
5n + 6n


X
1 · 3 · 5 · · · (2n − 1)
n=1

5n n!


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