1. Let a, = sin- - sin- for n eN = {1,2,3,...}. 1. Determine if the sequence {a,) converges or diverges. 2. Determine if the series an + converges or diverges.

Q: Give an example to show that a convergent series sum⟨x,ek⟩ek does not haveto sum to x.

A: First, let's understand the concept. A convergent series is a series whose partial sums eventually…

Q: Find the explicit formula of the following sequence. 8 (72, 24, 8, 3, ...} O a O b Oc - Od ƒ(n) = a₁…

A: Given sequence is 72, 24, 8, 83, ...

Q: (-1)"n For positive integer n, let an = 3" Determine whether the sequence {a,} is convergent.

A: Determine whether the sequence is convergent ?

Q: A sequence is said to be decreasing sequence if...... Vn>1 =S b O n+ 1 n n+1C O S 2n.d O n+1

A: Correct option :-  C Detailed Explanation

Q: The series (an - an+1) converges iff the sequence an converges. (Tips: Cauchy Criterion for Series)

A: We have to prove that, the series ∑n=1∞an−an+1 converges if and only if the sequence an converges.…

Q: Σ=on + 5") (-1)" 5n Find the sum of this infinite Series Σ=on +

A: Here we have to find the sum of given infinite series

Q: Suppose S = Ea, , s, is the n" partial sum of s, and the terms of the series n=1 n+1 2(3)** are…

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Q: write down the first five terms of each sequence

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Let > an be an infinite series. Choose the correct statements below. O If >, am converges, then >,…

A: The objective is to choose the correct statements.

Q: We want to determine if the sequence an = Using the ratio test we get that an+1 an 10" (3n)! is…

A:

Q: 2.152.All the expressions of an arithmetic sequence (a,) are positive and different from each other.…

A: Given : all the expressions of an arithmetic sequence an are positive and different from each other,…

Q: (a) Suppose that (în) is a sequence of real numbers. Define what it means to say that the sequence…

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Q: 1. Prove that the sequence {4+} converges to 4.

A: To know weather two function converge or not take difference of them and put limit to infinite. If…

Q: Doesthe series * 2n Converge or diverge フー一 30-2

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Q: 3. The power series x- 3 ....... can be expressed as +. 2n+1 8. a. 2n+1 =1 2n-1 b. E(-1)" 2n-1 n=1…

A: The power series is given by x-x33+x55+············ To evaluate : The summation notation of the…

Q: 1- 5: Express the following as sequence of the indicated terms: 1 Ea, +- 1. 2' 10 а, 'i+1 2. 3.

A: "Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Let {a} be a sequence with positive terms. Suppose that the series an converges to 3. n=1 Which of…

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Q: Indicate a general rule for the nth term of the sequence when a, = 2 and r =. 3. a, = (2)(J)*| n+1…

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Q: 1. Let a, = 1 and an+1 = 1+ 1+an (a) Find the first six terms of the sequence {an}. (b) Prove that…

A: As you asked multiple sub parts so I answered 1st three subpart.

Q: Evaluate th e relate series of each sequence. 1) -7,-5,-3,-1,1,3

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Q: 1. (1+n - n?)

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Q: 9.) Define what is the sequence {Xn} diverges n = ∞ as meant by to +00/-00

A: A sequence {xn} diverges to +∞ as n approaches infinity, it means that the terms of the sequence…