Question
Show that the set:
is not closed.
Answer :
Word Count : 111
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Consider the set [ S = \left{ \frac{1 + (-1)^n}{2} + \frac{1}{n} \mid n \in \mathbb{N} \right}. ] For even (n = 2k), (\frac{1 + (-1)^n}{2} = 1), so the terms are
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Related Questions
Discuss the convergence of the p-series by using the integral test.
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.
Find the radius of convergence of the series , where
.
Test the convergence of the series: .
मान लीजिए कि f तथा g, R[a, b] में हैं। तब दिखाइए कि फलन f + g भी R[a, b] में हैं, तथा .
श्रेणी के अभिसरण की जाँच कीजिए।
Using mathematical induction, prove that the sum of the squares of first 'n' natural numbers is .