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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
17-6  Calculus – Differentiation and Integration
Also if lim
n
n
s
→∞
= then {s
n
} is said to diverge to ¥ and if lim
n
n
s
→∞
= −∞ then {s
n
} is said to
diverge to .
If a sequence neither converge nor it diverges to or , then the sequence is said to be
oscillating. For instance, the sequence ( ) ,
{ }
1
n
n N neither converges nor diverges. It just oscillates.
Example 17.5 Show that the sequence 1,
1
2
,
1
3
,
1
4
,
converges to 0 using the limit definition.
Solution: The above sequence indicates that the terms are getting closer and closer to zero, as they move
along. From the definition of convergence, we need
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Publisher Resources

ISBN: 9789353948221