Question
If an infinite series converges, then show that
.
Answer :
Word Count : 80
Let (s_n=\sum_{k=1}^n a_k) denote the (n)-th partial sum. Convergence of the series (\sum a_n) means the ___ _____ __________ ________ _________ ____.
_________ _______ ________ ____ _________ _____ ________ _______ _________ __________ ____.
___ _______ ___ _________ __________ ___ __________ __________ ________.
________ ________ ______ _______ ________ ____.
______ ______ ____ ___ _________ ___.
___ _____ _______ _______ ______ ______ ____ ____ ______ ______.
____ _______ ___ _________ _________ ___ _________ ____ __________ _________ ________.
_____ _____ _______ _______ ___.
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Let (s_n=\sum_{k=1}^n a_k) denote the (n)-th partial sum. Convergence of the series (\sum a_n) means the ___ _____ __________ ________ _________ ____.
_________ _______ ________ ____ _________ _____ ________ _______ _________ __________ ____.
___ _______ ___ _________ __________ ___ __________ __________ ________.
________ ________ ______ _______ ________ ____.
______ ______ ____ ___ _________ ___.
___ _____ _______ _______ ______ ______ ____ ____ ______ ______.
____ _______ ___ _________ _________ ___ _________ ____ __________ _________ ________.
_____ _____ _______ _______ ___.
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Related Questions
Show that the function defined as
is continuous on its domain, but not uniformly continuous there. Will the function be uniformly continuous on
for any fixed c > 0?
Check whether the following sets are open or closed or neither:
(i)
(ii)
जाँच कीजिए कि निम्नलिखित समुच्चय विवृत हैं या संवृत हैं अथवा न तो विवृत हैं और न ही संवृत।
i.
ii.
उपयुक्त प्रति उदाहरण देकर इस कथन को असिद्ध कीजिए:
प्रत्येक तथा
के लिए
है।
Give one example for each of the following. Justify.
(i) A set which is neither open or closed.
(ii) A set which has no limit point.
Check whether or not the sequence , defined by:
and is convergent.
मान लीजिए कि f तथा g, R[a, b] में हैं। तब दिखाइए कि फलन f + g भी R[a, b] में हैं, तथा .
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