Module 1
:
Real Numbers, Functions and Sequences
Lecture
2
:
Convergent & Bounded Sequences [ Section 2.3 : Bounded Sequences ]
Practice Exercises 2.3: Bounded Sequences
(i)
Let
and
be bounded sequences. Prove that
and
are also bounded sequences. What can you say about the sequence
(ii)
Give examples to show that if
and
are bounded sequences,
for every
,
then
need not be a bounded sequence.
(iii)
Let
be a bounded function and
be any sequence. Is
a bounded sequence? Justify your claim.
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and 
be bounded sequences. Prove that 
and 
are also bounded sequences. What can you say about the sequence 
for every 
, 
need not be a bounded sequence. 
be a bounded function and 
a bounded sequence? Justify your claim. 
