n3 + 5n 8n2 + 5n + 1 4- n=1 (A) diverge (B) converge 1 5- (A) diverge (B) converge n( Inn)² n=2

Q: (-1)³ 3j² + 5j

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Q: 3n! 3n! Find lim State whether 2n=1 converges or diverges. n→∞ 4n!-1) 4n!-1

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Q: If An converges and an > bn, then bn also converges. n=1 n=1

A: To find  Whether the given statement is true or false.

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Q: Q1- n? - 7n+3 Determine whether sequence convergent or divergent. |1+10п -4n? n=3

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Q: Vn3 + n2 + 1 Determine whether the series converges or diverges. E1 n2 -n+3

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A: given∑n=1∞=-2n2+2n-1-4n3+4n2-2n-2find if convergent or divergent

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Q: What is the difference between formulas of order of convergence O(h^k) and these of o(h^k)?

A: The difference between formulas of order of convergence O(hk) and o(hk) is discussed below.

Q: 2 4n = (z - 6)° + (z- 6)* (т — 6)° 25 - 3! (x – 6)8 125 - 4! +... 5- 2! Find an expression for an an…

A: Question is solved.

Q: For each of the following, prove whether the series converges or 1. 2j+1 3j² - 2 diverges.

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Q: 2x-1 Q7. Find the convergence interval and radius of the series : 2 (-1)" . Σ(-) 2n-1 n=1

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Q: Check for convergence / divergence. Find the limit if convergence. 3n²-5n+1 2n +7 0 {a}= (a.} =…

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Q: state whether the series converges or diverges. Please provide an explanation as to why

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Q: (-1)" • Series: Test: Comparison Test n n=1 (a) If the Test Applies: (i) Comparator: (ii) Choose…

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Q: (2n)! a"(n!)2 A) diverges if |a| 2² n-1 C) converges if |a| > 2ª

A: Here we have to find the converges or diverges of the given series.

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A: We have to find the given series is convergent or divergent by ratio test.

Q: series converges or diverges.

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Q: Σ n=1 (-8)" - (-8)^ – I convergent O divergent If it is convergent, find its sum. (If the quantity…

A: This series is Converges

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Q: n² +1 8. is The sequence 2-n2 n =1 n=1 Select one: a. Divergent b. Convergent

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Q: Determine wheter the sequence convergesor diverges. If it converges, find the limit. a)…

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: j=1 2j-1 3j³ - 2

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Q: Sequence: Converges or Diverges? If converges, find the limit. 5n – 1 n an = 5n +1

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Q: Advanced Calculus: Suppose {xn} is a sequence of real numbers that is (i) increasing (that is, xn…

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Q: n-1 (a) n+1 Converges or Diverges: limit (If Converges): (b) Ž"-1 n=1 N+1 Converges or Diverges:…

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Q: n=1 3n²+5n 8-7n² Does this converge or divenge? Explain your answer

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Q: Q4/Find the value of b which I+ ė + ĕ -6. %3D Qn! For what value of r does the infinit Series Sn…

A: Recall: Infinite Geometric Series : Given that an Infinite Geometric series               a+…

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Q: th 15. A certain series has an n" partial sum given by S, = a, +a, + • + a, Which of the following…

A: We have to choose the correct option.

Q: 1. Find the value № such that the partial sum 6-k estimates the infinite sum ∞ N n=1 n=1 6-k with an…

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Q: -k + 4 k2 – 11 Consider the series (a) Find the first three terms in the sequence of partial sums.…

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Q: Sequences versus series {(- a. Find the limit of the sequence 5 4\k b. Evaluate 2 k=0

A: a. Given: The sequence -45k To find: The limit of the sequence.

Q: 2x-4 x²-4x+3 1. Express the function f(x) fractions. Find the interval of convergence. = as the sum…

A: Here, the given function is: f(x)=2x-4x2-4x+3

Q: 6. 3n2 + 2 n=1

A: We will use Comparison Test to check whether the series is convergent or divergent

Q: Real Analysis Prove that series 1/n(n+1) converges

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A: The set of all x-values at which the power series converges is called the interval of convergence.…

Q: j=1 (−1)ª 3j² + 5j

A: Given series is ∑j=1∞−1j3j2+5j. Alternate series test:- Let an be a sequence of positive real number…