Lebl-Basic-Analysis-I · Problem 6.1.14

Sequences of Functions

Mathematics · geometric-series-uniform-convergence

Problem

(requires §2.6) In Example 6.1.3 we saw ∑k=0∞xk\sum_{k=0}^\infty x^k converges pointwise to 11−x\frac{1}{1-x} on (−1,1)(-1,1). a) Show that whenever 0≤c<10 \leq c < 1, the series ∑k=0∞xk\sum_{k=0}^\infty x^k converges uniformly on [−c,c][-c,c]. b) Show that the series ∑k=0∞xk\sum_{k=0}^\infty x^k does not converge uniformly on (−1,1)(-1,1).

Related theory

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