-1)". 5n n=1 is convergent to 1 is convergent to – This option This option is convergent to is divergent 6.

Q: |an also converges because 0 If an converges then < lan|, for n = 1, 2, ... n=1 n=1

A:

Q: If 2a, converges, then 1. diverges Select one: True False

A: Use the defination of convergence of a series.

Q: Discuss the Conditions foo which Foudies Segies is convergent?

A: Given: Conditions of Fourier series is convergent.

Q: 3 converges conditionally because lim n - 3 = 0. 3n + 1 3n + 1 True False

A: The given question is solved with explanation below.

Q: 1 converges conditionally because lim 第-1 = 0. 2n n=1 True False Reset Selection

A: this is false becuse

Q: If 2n=1a, converges, and if a„ # 1 and a,n > 0 for all n, a. Show that E=1a, converges. b. Does…

A:

Q: I. Consider an = V4n² + 3n – 2n for n >1. 1. Determine if {an}-1 is convergent or divergent. 2. Is >…

A: Simplify the expression of an. Multiply and divide the given expression of an by 4n2+3n+2n to…

Q: The following improper integral (7x-5) (x+3)(x²-x+1) converges to In(2) diverges This option This…

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Q: 8. Determine by the ratio test if 2n=1 (2n)! converges or diverges.

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Q: converges, because 0 < 1 and an %3D debook 2n + 1 2n +1 2n +1 Room

A: We have to choose the true or false

Q: find the value of p which the inegrad converges absauaysconditionally COSY

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Q: 1 Determine whether (-1)". converges conditionally, absolutely, or not at all. Vn2 + 1 n=0

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Q: (-1)ªn n² + 1 mula converges to a value or diverges withou

A:

Q: N! 9) Show that converges/diverges

A: Use D Alembert ratio test

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: 7N 8N 3) Show that converges/diverges.

A:

Q: (3) Find all p ER so that 3n² + 2n +1 n2p-1 + 137 n=1 converges. As always, your answer must be…

A:

Q: If C.)" converges, then C,)" converges. n=0 n=0 Select one: True False

A:

Q: 6. Suppose a, converges. Assume the terms a, are non-zero. Prove ÷ diverges if it is true. n=1 n=1…

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Q: The series 7 2n E,(-1)" 4 n= is absolutely convergent. Select one: True O False

A: Root Test : Suppose we have series ∑ an .Define,                          L = limn→∞ an1n .Then ,(…

Q: Show that E-2 ((In n)ª/n²) converges for -o 1. n=2

A:

Q: Suppose that dz converges. What can we conclude about the constant p? Op>1 Op Op< 3

A: Explanation of the answer is as follows

Q: a n+1) %3D 2n Ans. Converges, 6)

A: Since you have posted a multiple  question according to guildlines I will solve first (Q6) question…

Q: Determine if >n=1 (-1)" is absolutely convergent or conditionally divergent. 4n 4 +1

A: First check for Absolutely convergence using Series Integral Test

Q: is convergent Vn3 + 4n + 5 or divergent. n=1

A:

Q: If 2 a, converges, then la,| diverges. n=1 n=1 True False

A: Given statement is FALSE. I HAVE given a counter -example.

Q: (- 1)"+(- =D1 converges conditionally in elect one: True

A: Please refer to the image below

Q: 1 3. En=1 (2n+1)3

A:

Q: n=1n2 +1 converges using 2 n =1 diverges using n =1 converges using 2 n =1 diverges using n =1 else…

A: Infinite series is the sum of the infinite sequence. A series is convergent if the sequence of…

Q: If an < bn and if En=1 an converges, then 1 bn also converges. True False

A: we can solve it by using comparison test.

Q: 13. Determine whether ∞ Σ(-1)* k1/2 k=1 converges absolutely, converges conditionally, or diverges.

A: The given series,    ∑k=1∞-1kk12

Q: n2 + 5n + 2 Determine whether converges abso- (1+ )" lutely, converges conditionally, or diverges.…

A:

Q: The series 2(k+2)3-k is k=1 convergent to 6 divergent convergent to 8 O None 15 convergent to 2

A: Given - A series To find - Nature of Series , i.e. Convergence or Divergence

Q: d) If Can's Converger and {b,'s diverges, Hhen fanton} Converges.

A: we argue by contradiction: suppose that an+bn converges. Since an converges by assumption, the…

Q: 1) (am) is not convergent but (a,(a, - 2)) is convergent.

A:

Q: 34. Assume that an+1/an converges to p = 4. -1 Does > an converge (assume that n=1 An # 0 for all…

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Q: 3 If Xn 4 and ly,l0. Select one: True O False

A: Given, xn → 4  and  yn≤31n2n for all values of n To determine whether ∑ xnynp  is absolutely…

Q: converges, then C„-)" " con COr n=0

A: We have to choose the correct answer from the given option according to the given series

Q: A) diverges B) converges

A: If the limit exists and is a finite number, we say the improper integral converges . If the limit is…

Q: Determine if the given is convergent or divergent. I In"(n*) 23n2 n=1

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Q: If conditionally converges then Jan| converges. 2=1 n=1 True False Rationale:

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Q: Prove 2^1/n infinity n=1 is convergent

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Q: If Ea, converges absolutely, prove that Ea,² converges.

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Q: 1dx x²+2x+5 -00 O diverges O None 37 converges to 4 converges to converges to converges to 3r

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Q: Show that 2"x" converges if |x| <. n=1

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Q: If 2(-1)" a, is absolutely convergente the n=0 na, is divergente. Select one: O True O False

A: Topic:- sequence and series

Q: (-1)"(7n + 1) Does En=1 converge or diverge? (3n + 1)

A: Alternating series test: If infinite series is If any of these two conditions does not hold, then…

Q: (4) Suppose {a„}1 converges to L and that a, 2 0 for all n. Prove that {Van}1 converges to L. Tip:…

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Q: 1.4 Does (fa(r)} in 1.3 converges uniformly on |-3,3]? Explain.

A: