9. Test each of the following series for uniform convergence on the indicated interval: sin(2kr) * e^(2k + 1)n b^(2k) * lnx
Added by Irene D.
Step 1
Let M = 1 / (2k + 1)n, then |sin 2kx / (2k + 1)n| ≤ M for all x and k. Since ∑M converges, by the M-test, the series converges uniformly on [-a, a] for any a > 0. For the second series, b2k / (1 + |x|)k, we can also use the Weierstrass M-test. Let M = b2k / 2k, Show more…
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