Let an 6n 2n + 1 (a) Determine whether {a} is convergent. O convergent divergent = (b) Determine whether Σ n = 1 convergent O divergent a, n is convergent.

Q: determine if convergent or divergent first please!

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Q: an = In(n+1) – In(n) for n E N determine if the following is convergent or diverge An

A: limn→∞an=limn→∞ ln(n+1)-ln(n)=limn→∞ lnn+1n=limn→∞ lnn(1+1n)n

Q: 8WI (-1) 3n+6 O Absolutely Convergent O Conditionally Convergent O Divergent

A: The given series .To determine the series absolutely convergent, conditionally convergent, or…

Q: n3 Determine the convergence or divergence of n=1 n7 + 2n² + 1

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Q: 1 1 Зп — 1 3n + 2 n=1

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Q: et the sequence {xn} satisfy | Xn+1-Xn 0 Show that ● |xn-Xn+k|≤|xn-Xn+1| + | Xn+1 - Xn+2+...+…

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Q: Σ(-1)^+¹ Test k=1 1 for absolute/conditional convergence

A: The given series: ∑k=1∞-1k+11k5 .We need to test for absolute onvergence and conditional…

Q: 1 Prove that Σn=1 4² converges uniformly on R.

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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: Spow it the arics is absolutely convergent, conditionally convergent, or diverg ent. (using…

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Q: =

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Q: Consider an = V4n2 + 3n – 2n for n 2 1. - (a) Determine if {an}, n=1 is convergent or divergent (b)…

A: Here, an=4n2+3n-2n, n≥1     =4n2+3n-2n4n2+3n+2n4n2+3n+2n     =4n2+3n-4n24n2+3n+2n     =3n4n2+3n+2n

Q: ne if it es or rges 2. Σ n=1 2n n use monotor convergence theorem

A: Convergence of the series

Q: 2. 8[][

A: The objective of the question is checking the convergence or divergence of the given series.

Q: Show that if ak is absolutely convergent and |bx| < |ak| for all k, then E bk is absolutely…

A: Explanation of the answer is as follows

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

A: Alternating series test

Q: x +x2+..+ xn Let 0 is convergent, show that is convergent or divergent (2)Let is convergent, show…

A: (a) Given that an=x1+x2+...+xnn, bn=x1x2...xn1n It is known that bn≤an Since an is convergent. By…

Q: Define 1 1 + (−1)n-1 an = 1 - ln 2. 2 3 n Show that 1 an converges and determine its sum. n=1 +

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Q: Exercise 1. Let an 2n 3n+ 1 (a) Determine whether (an) is convergent. (b) Determine whether an is…

A: Part (a) A sequence an is said to be convergent if limn→∞an exists and is finite. Determine limn→∞an…

Q: (2) If £ an and D bn are both divergent then is E an · bn necessarily divergent? If yes, provide a…

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Q: Let an be recursively defined by ao = 2, an+1 = (an+1) for n>0. Show that an converges, and find its…

A: Given: A sequence a0=2 , an+1=14an+1. To Show: The given sequence is convergent and also find the…

Q: 1. Σ 4n2 in 8n +3

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Q: n - 1 converges absolutely because lim - 2 (n – 1) R=1 True O False Reset Selection

A: Consider the given series.

Q: an = In(n+1) – In(n) for n EN determine if the following is convergent or divergent { an } n=1

A: Solving