(2) Σ3 n=1 (b) Σ n=1 (0) Σ n=1 (e) (−1)n-¹ n (n + 2)3 n-1 n-1 η2 + 2n en n!√n (1) Σ n=1 f In(n)

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A:

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Q: а) x(0)--1,х' (0)-8 b) × () = },x (?) = o

A: x(t) = c1cost + c2sint . x '(t) = - c1sint + c2cost . x(0) = c1 = -1 . x '(0) = c2 = 8 . Thus, the…

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Q: o Show that series is convergent is not absolutely convexgent but coNerse geueral. twe Yn

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A: Comparison test: If limn→∞anbb=positive and finite then both an and bn are convergent or divergent.…

Q: Let > an be an infinite series. Choose the correct statements below. O If >, am converges, then >,…

A: The objective is to choose the correct statements.

Q: = {()}. 2n 1 2n +1) T2 a) {a,} -

A: Given: To determine the series converges or diverges as follows, an=2n-12n+1n

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A: To Show : X is complete if and only if every absolute convergent series in X converges.

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Q: Consider an tan -1n • Determine if the sequence {an}=1 converges or diverges. n=] • Is the series an…

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Q: 1. Let a, = sin- - sin- for n eN = {1,2,3,...}. 1. Determine if the sequence {a,) converges or…

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Q: Give an example of a conditionally convergent series an such that Σna, con- n=1 n=1 verges.

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Q: x +3, (x + 3)2 + 22 1+- 32

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Q: 2.Determine whether the following sign series is divergent or absolute convergence or conditionally…

A: The given series is  ∑n=1∞ -1n+12n-13n+4