Limit superior and limit inferior supremum and infimum csir Net June 2017 real analysis

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Sequences and Series of Real Numbers: Sequence of real numbers, the convergence of sequences, bounded and monotone sequences, convergence criteria for sequences of real numbers, Cauchy sequences, subsequences, Bolzano-Weierstrass theorem. Series of real numbers, absolute convergence, tests of convergence for series of positive terms – comparison test, ratio test, root test; Leibniz test for convergence of alternating series.
Functions of One Real Variable: Limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L'Hospital rule, Taylor's theorem, maxima, and minima.
Functions of Two or Three Real Variables: Limit, continuity, partial derivatives, differentiability, maxima, and minima.

Real Analysis: Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets, completeness of R. Power series (of real variable), Taylor’s series, radius and interval of convergence, term-wise differentiation, and integration of power series.

Comments
Use LH rule
lim(n tends to infinity) e^n((-1)^n/n= e^(1,-1)

Limit superior and limit inferior supremum and infimum bounded Sequence Net June 2017 mathematics

En Net June 2017, 22
Key (d)