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Tag Archives: series
Basic Analysis: Uniform Convergence
Once again, let be a subset. Suppose we now have a sequence of functions , where n = 1, 2, 3, … , such that for each x in D, the sequence converges to some real value. We’ll denote this value by f(x), thus … Continue reading
Posted in Notes
Tagged advanced, analysis, continuity, convergence, pointwise convergence, series, uniform convergence
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Basic Analysis: Sequence Convergence (4)
In this article, we’ll consider the convergence of an infinite sum: . We call this sum an infinite series. Let be the partial sums of the series. Definition. We say that is L (resp. ∞, ∞) if the partial sums converge to … Continue reading
Posted in Notes
Tagged abel transformation, alternating series, analysis, basel series, convergence, series, telescoping series
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