Exercise 7. Use Weierstrass' test to determine sets on which the series converges absolutely uniformly. (1– 22)" sin(nr).

Q: -Show how the series converges absolutely COS s (3n + 1) n5 +4 N3D1

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Q: 19. Give an example of divergent series E ak and E, bu such that the series E akbk converges.

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Q: 21. Show that E(-1)"+1; 2n converges n! absolutely. n=1

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Q: 7.- Prove that the series n=1 n³ n4 1 is divergent.

A: We have to prove the given series is divergent.

Q: En-o(1 +)" CO 5n ii) 2n-0 100 (Зп)!

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Q: Solve Σ 0 to ∞ ((n! • x^n)/ n^n) for x = e and x = -e and explain whether each point converges or…

A: Solve for x = e and check whether it converges or diverges as follows.

Q: From Rogawski ET 2e section 10.5, exercise 7. Apply the Ratio Test to determine convergence or…

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Q: 4. Consider a power series of the form E anx". Suppose that lim sup Jan|/n = 0. Prove that the…

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