4. Consider the seriesΣ(−1)²+1n=12 sin(nx)n(a) Show that the series is uniformly convergent for x = [8, π – 6] for 8 € (0, π).(b) Show that the series is convergent for x = [-, π].(c) Is the convergence uniformly on [0, π]?

(a) Show that the series is uniformly convergent for for by using the Dirichlet test for uniform…

Answered: Consider the series Σ(-1)n+1 n=1 2…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider the series Σ(-1)n+1 n=1 2 sin(nx) n (a) Show that the series is uniformly convergent for x = [8, π – d] for d = (0, π). (b) Show that the series is convergent for x € [-, π]. (c) Is the convergence uniformly on [0, π]?