2. Assume that p > 1. (a) For all n> 1 prove that P-1 (n + 1)P (b) Prove that is convergent. NP < n¹−² − (n + 1)¹-p -P

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: V2+cos (n2+1) Use the basic comparison test to determine whether E1 n=D1 converges or n+en diverges.

A: To check the Convergency of the given series. We apply here Simple comparison Test and Ratio Test of…

Q: (b) Determine whether Σ n=1 ditionally, or diverges. (-1)n.n²+3 n²-4 converges absolutely, converges…

A:

Q: . Find all values of x for which пх" n=1 (n + 1)(2x + 1)" converges absolutely.

A:

Q: 3n The two convergent subsequences of the sequence (-1)+2 is

A: xn=(-1)3n+2 x2n=(-1)3(2n)+2=(-1)6n+2x2n-1=((-1)3)2n-1+2=(-1)2n-1+2    as (-1)3=-1

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

A:

Q: Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is…

A:

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

A:

Q: Solve all 1) Assume that (xn) is a monotone decreasing and bounded sequence. Prove that (xn) is…

A: is monotone decreasing and bounded sequence.We have to prove that  is convergent.

Q: The two convergent subsequences of the sequence (-1)™+2 is a) x, = (-1)" +2 and x, = +2 %3D 2n+1 6n…

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Q: Let X = (xn) be a positive sequence of real numbers. Show that if x₁ + x₂ + + In Yn n then yn is…

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Q: (a) Let a, = 1 and ant √1+a, for all ne N. (i) Show that {a} is increasing and bounded above by 2.…

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Q: (-1)*+a 2 4. Determine if converges. 2n - 5 (n +1)² + 5

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Q: (-3)" converges or diverges. Vn Determine whether n=1

A: ∑n=1∞-3nn Here, an=-3nn

Q: (b) Determine whether n=1 ditionally, or diverges. (−1)n.n²+2 (n − 1)! converges absolutely,…

A:

Q: Q3 A) Write the first five terms of the following: - 2. {1- (-1)") (3n+2 B) Determine which of the…

A: "since you have asked multiple question,we will solve first question for you.If you want any…

Q: 7n Let an %3D 8n + 1 (a) Determine whether (a,) is convergent. convergent O divergent DO (b)…

A: