Question
Give one example each for the following. Justify your choice of examples.
i) A sequence which is divergent.
ii) A set which is neither open nor closed.
iii) A compact set.
iv) A set which has no limit point
Answer :
Word Count : 193
i) A sequence which is divergent: Consider the sequence $a_n = n$, i.e., $1, 2, 3, 4, \dots$. This sequence is divergent because as $n \to \infty$, $a_n \to \infty$ and it _____ ________ _____ __________ ________ ______ ______ _____ _____ ________ ___ ________.
________ _______ ______ ___ ___ ____ ____ ________.
______ _________ __________ ____ _____ _________ __________ __________ ________ _________.
_____ ________ ___ ____ ________ ________.
____ _____ _____ _____ ______.
_____ __________ ______ ______ _______ ___ __________ ____ ___ ______ _______.
_____ ______ ______ ____ ______ _________ __________ ______ ____ ___ _____ ____.
____ ____ ___ _______ ________ ______ _________ ____ __________ _________ ____.
__________ ____ ___ _____ __________.
________ _______ ____ _______ ______.
____ _____ ____ _____ _________.
________ _____ _______ ________ _____ __________ _________.
________ ____ _________ _________ _______ ____ ______ _________ __________.
_____ ____ ________ _______ __________ ____ _______ ___.
___ __________ ____ ______ __________ ___ _______ ______ _____ _________ _________.
____ __________ _________ _________ __________ ______ _________ ____.
_____ __________ _________ __________ __________ ___ _________ _____.
_____ ________ ________ ________ _________ ____ ____ _______ ___ _____ _________.
________ ____ ________ ____ ________ __________ ____.
__________ _______.
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i) A sequence which is divergent: Consider the sequence $a_n = n$, i.e., $1, 2, 3, 4, \dots$. This sequence is divergent because as $n \to \infty$, $a_n \to \infty$ and it _____ ________ _____ __________ ________ ______ ______ _____ _____ ________ ___ ________.
________ _______ ______ ___ ___ ____ ____ ________.
______ _________ __________ ____ _____ _________ __________ __________ ________ _________.
_____ ________ ___ ____ ________ ________.
____ _____ _____ _____ ______.
_____ __________ ______ ______ _______ ___ __________ ____ ___ ______ _______.
_____ ______ ______ ____ ______ _________ __________ ______ ____ ___ _____ ____.
____ ____ ___ _______ ________ ______ _________ ____ __________ _________ ____.
__________ ____ ___ _____ __________.
________ _______ ____ _______ ______.
____ _____ ____ _____ _________.
________ _____ _______ ________ _____ __________ _________.
________ ____ _________ _________ _______ ____ ______ _________ __________.
_____ ____ ________ _______ __________ ____ _______ ___.
___ __________ ____ ______ __________ ___ _______ ______ _____ _________ _________.
____ __________ _________ _________ __________ ______ _________ ____.
_____ __________ _________ __________ __________ ___ _________ _____.
_____ ________ ________ ________ _________ ____ ____ _______ ___ _____ _________.
________ ____ ________ ____ ________ __________ ____.
__________ _______.
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Related Questions
निम्नलिखित श्रेणियों के अभिसरण की जाँच कीजिए :
(i)
(ii)
Let f : R → R be a function defined by:
Check whether f ′ is continuous on R.
सिद्ध कीजिए कि फलनों का अनुक्रम {fn} जहाँ
रीमान समाकलन से परिकलित कीजिए।
Prove that between any two real roots of ,2 e cos2x = x there is at least one real root of ex sin
Show that the set:
is not closed.
निम्नलिखित कथन तथा उनके निषेध को तर्कसंगत प्रमात्रकों का प्रयोग करते हुए आप किस प्रकार प्रस्तुत करेंगे? निषेध को शब्दों में भी दीजिए।
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