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