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Calculus: Differentiation and Integration, 1st Edition
book

Calculus: Differentiation and Integration, 1st Edition

by ICFAI
April 2024
Intermediate to advanced content levelIntermediate to advanced
710 pages
20h 50m
English
Pearson India
Content preview from Calculus: Differentiation and Integration, 1st Edition
Infinite Sequences and Series 17-21
Consider Σ Σv
n
n
=
1
2
, which is a geometric series, with common ratio
r =
1
2
0 1( , ).
Since Σ Σv
n
n
=
1
2
is convergent, by comparison test, S
1
n
n
is also convergent.
Example 17.27 Test for convergence
n
n n
n
2
3 2
1
=
sin
.
Solution: Let u
n
n n
n
=
>
2
3 2
0
sin
for all n. This is a series of positive terms.
We know that
n
n n
n
n
n
2
3 2
2
3
1
> =
sin
as n gets larger.
Consider
Σ Σv
n
n
=
1
.
It is seen that the above series is harmonic series and we proved earlier that it diverges.
Therefore, by comparison test,
n
n n
n
2
3 2
1
=
sin
is also divergent.
Example 17.28 Test for convergence
1
2 10
3 2
1
n n
n
+
=
.
Solution: Let u
n n
n
=
+
>
1
2
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Publisher Resources

ISBN: 9789353948221