## Transcribed Text

1. Given the sequence definitions, answer the following:
a) an - 3n+2 , write out the first three terms.
4n-1
a1 =
a2 -
a3 =
Does the sequence converges or diverges? If it converges, tell what value it converges
to
b) b1 = 2,b2 - 1.6n - bn-1 + write out the first three terms.
b1 =
b2 =
b3 =
Does the sequence converges or diverges? If it converges,
tell
what
value
it
converges
to.
2.
Does the improper integral 500 - 2 da converge? Show your work
3. Find the sum of the following series if it is converges, otherwise state that it diverges.
a)
8
3n+(-1)n
n=1
4n2
b) \
80
4
n=2
n2 - 1
4. State whether (You do not have to prove) the following statement are TRUE(T) or FALSE (F). If it is false give
an counterexample.
a) For the series [n-1 an. if limn too an = 0. then the series converge.
b) Alternating series always converges.
c) If a series converges then the series formed by taking the absolute values of the terms is guaranteed to
converge.
d) For the integral test to work, the corresponding function should be increasing eventually.
e)
Any series that can be tested for convergence using the Direct Comparison Test, can always be tested
using the Limit Comparison Test.
5. Use the Direct Comparison Test (DCT) or the Limit Comparison Test (LCT) as appropriate to test the
convergence of the following series:
a)
8
In n
n
n
80
n² +sin n
b)
n=. 1
3n7 +5n-1
6. Use the Alternating Series Test (AST) or any other test to check the convergence of the following S
a) [n-3 (-1)" n 7n2- 5
21n² +n
b) [no,1 (-1)n-1
n
n2+4
7. Use the Integral Test to check whether the following series converge. Show you work.
00
Ln-1
4
Extra Credit Problem (8 points): Only answer any two parts. Test whether the following
series
are
convergent. Mention the test you use and clearly state your conclusion.
12
80
a)
n=1
(1 - 3
k
b)
00
k=1
2020
(-))
n=5 8
3 cos(3n)+2
2n
00
4rn-5n+3
tan
n=]
12n°+7n2-2020

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.