Calculus II Quiz Questions please do all the questions with showing all details of your work please try to use simple and clear way of solving calculus pro

Calculus II Quiz Questions please do all the questions with showing all details of your work please try to use simple and clear way of solving calculus problems. [1]
2
Let an =
n
(a) Is the sequence {an} = {} convergent? If yes, to what does it converge?
(b) Is the series oo
2n=1 an
analconvergent? If yes, to what does it converge?
2
[2]
Determine whether the sequence {an} converges or diverges. If it converges, find
the limit.
(a) an = 2 –
– (0.35)”
(b) an
COS
(c) an = cos
(d) an
= 3-ncos
(e) an =
2n2+vn
n-3n2
3
[3]
Determine whether the series is convergent or divergent. If it is convergent, find the sum.
Hint: think geometric series
oo
(a) Σn=1
en
3n-1
(b) In=1[(0.8)n-1 – (0.3)”]
[4]
Find the values of p, if any, for which the series is convergent.
En=3 n ln(n) {]n[ln(n)}}P
4
[5]
Can the Integral Test be used to determine whether the series is convergent or divergent?
If yes, determine whether the series is convergent or divergent. If no, say why?
(a) Ση=1
5oo (-1)” n3
n4+1
(b)
Σn=1
(-1)2n n3
n4+1
5
[6]
Consider the series
00
(x – 4)”
32n
n=0
(a) Find the values of x for which the series converges.
(b) Find the sum of the series for those values of x.
6

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