Let S = (1 + (nx)²)-¹. a. Show that the series S converge on R\ {0}, but does not uniformly converge on this set. b. Show that if a > 0, the series uniformly converges on R\(-a, a).

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Q: l x such that the

A: Here we have,  A=∑n=0∞(-3)nxnn+1=∑n=0∞an ⇒an=(-3)nxnn+1

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Q: 2. Show that the series is conditionally convergent. n=2 cos(nx) √n ln n

A: Solution of the problem as follows

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A:

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A: Explanation of the answer is as follows

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A: To apply root test, we transform given series to new series where x is taken arbitrary.

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Q: series converge

A: Please check the next step

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