Which of the followings are true? 1. E (-1)" is absolutely convergent. m-D1 n+inn II. En-1 2" (-1)8r is conditionally convergent. III. (-1y"-1 is conditionally convergent. IV. En-l (-i"n is conditionally convergent. n+? O a. II, IV O b. I, II

Q: Which of the followings are true? 1.En=1 7?+Inn (-1)" is absolutely convergent. II. >n=1 (-1)m is…

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Q: Which of the followings are false? I. 0 (-1)" is absolutely convergent. Ln=1 n² +Inn 2n II. E (-1)…

A: we have to check each options

Q: (x-2) What is the convergency interval of O aR O b. [1,3] O (1,3) O d. (-1,5) O e (-1,5]

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Q: Let a, = (-1)" + -, vn 2 1. Which of the statements below is/are true? I: Ja,|S 2, Vn 2 1 II: lim,-…

A: There are two properties for a sequence to be convergent, and they are as follows: Monotonicity…

Q: - -I -1- + 1 -1- F1 1,0 0.2 The sequence s, graphed is decreasing and lim sn = 0 Find the smallest…

A: Here is the solution of the given problem:  Sum of a Series:

Q: Two of the following statements are true. Which ones? 8 If Σen (*1- x0)" converges, then en (x-xo)"…

A: Note that first and last option of your questions are same.

Q: Rigorously show that (-1)"-1. n2 +1 is conditionally convergent. n=1

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Q: Which of the followings are false? 1. E (-1)" Ln-1 n+ Inn is absolutely convergent. 2n (-1)* 2…

A: We have to choose the correct answer

Q: Two of the following statements are true. Which ones? 8 If Σen (1-xo)" converges, then cn (x-xo)"…

A: statement 1 if ∑n=0∞cnx1-x0n converges then ∑n=0∞cnx-x0n converges for all x such that…

Q: Which of the following is the generating function for the sequence 5,5, 5,5? O A. G(x)=(1-x) 1 O B.…

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Q: 00 dz Vr² + 11z + 19 00 I + 11 1³ + 11x² + 71 IP- 1

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Q: Q5. Find the linear convolution of the following two sequences x(n) [3,11,7,0,-1,4,2] -3sns3; h(n) =…

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Q: an = aq"; bn = (-3)", dla n ≥ 2 oraz bo = b₁ = 0; 2n Cn = dla n ≥ 2 oraz co = 1, c₁ = 2. n!'

A: As per the question we are given three sequences : an , bn , cn  And we have to find their…

Q: 4n2-11 Q2. Determine if the sequence converges, and if so find its limi 12n2+4n-8.

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Q: 16. [(−1)² +1] 2 a. converges to b. converges to 7~ e. diverges 4 1 2 c. converges to 1 d. converges…

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Q: The. negation of (an) convergent is: a. Va, 3V, VN,3n > N: an € V b. 3a, VV,3N, Vn 2 N: an € V c.…

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Q: (-1)" ( b) Σ 2n Test: diverges converges n=0 Reason: (e) * (1+ 4)" Test: diverges converges n=1…

A: Alternating series test

Q: 40. Which of the following functions can be used to find the nth term of the sequence 6, 11, 16, 21,…

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Q: n2n n=1 (1+n)³n converges O diverges

A: It is given that ∑n=1∞ n2n1+n3n. Denote the general term of the series by un.  un=n2n1+n3n. Use…

Q: Which of the followings are true? 1.En 1 nInn (-1)" is absolutely convergent. 11. En 1 (-1) is…

A: Option (e) is correct.

Q: Let an > 0 and assume that an diverges. Write Sn = a1 + a2 + • ·.+ an. Prove the following…

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Q: Let ³ 10n 4n + 1 Determine whether is convergent.

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Q: 1.3. . (2n – 1) 2.4... 2n ... Prove the sequence an = has a limit.

A: Note the results : Theorem 1: A monotonic increasing sequence which is bounded by above is…

Q: What are all of the values of x, such that converges?

A: We have to use GP sum Common Ratio.

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.