SOLUTION: MATH 208 City Colleges of Chicago Harold Washington College Calculus Questions

SOLUTION: MATH 208 City Colleges of Chicago Harold Washington College Calculus Questions.

View attached explanation and answer. Let me know if you have any questions.20,19,18, 17, 16
View attached explanation and answer. Let me know if you have any questions.All done
View attached explanation and answer. Let me know if you have any questions.

( 20 )  ( −1)

n

arctan ( n )

n =1

b
n =1

n

, bn =

n

3

; an =

arctan ( n )
n

3

; f ( x) =

x3

1
, which is a converging p-series
n3

arctan ( n )  n
a

lim n = lim
= lim arctan ( n ) =
3
n → b
n →
n →
2
n
n
3

Thus, by Limit Comparison Test, the series

the series

arctan ( x )

 ( −1)

n

arctan ( n )
n3

n =1

( a finite real number )

arctan ( n )

n =1

n3

converges which means

is absolutely convergent .

 1 
 1 
tan 
 ; an = tan 

n =1
 n
 n

1
bn , bn =
, which is a diverging p-series

n
n =1

(19 )  ( −1)

n

 1 
tan 

an
n

lim = lim
n → b
n →
1
n
n
1
Let
= t then n →   t → 0.
n
tan ( t )
a
lim n = lim
=1
n → b
t →0
t
n

Thus, by Limit Comparison Test, the series

n =1

the series

 ( −1)
n =1

n

 1 
 diverges which means
 n

 tan 

 1 
tan 
 is not absolutely convergent.
 n

Now, for n  1,
1
1

n +1
n
 1 
 1 
tan 
  tan 

 n +1 
 n
an +1  an
a…

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SOLUTION: MATH 208 City Colleges of Chicago Harold Washington College Calculus Questions

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