Determine the behavior of the following SEQUENCES. 3n+sin(n² } The sequence The sequence The sequence n 3n {(-9) {(−1)² diverges diverges n² +6n+21 9n²2n 6 diverges

Q: (a) the boy con only make UP pnd Right moves anly he de food? the How many parths (b) If he mandemly…

A: We will use basic logic to answer both parts. Note that in the question post, only two parts named…

Q: 4か さ n=0

A: To determine whether the given sequence converges or diverges.1+4n4nn=0∞

Q: 1 {4 +

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Q: n" 3) > (-3)2n n=1

A: We apply here root test.

Q: (n2 +1)2 n=1 2.

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Q: E (1) (-1). Incn) Incn) + l000 ne50

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Q: Let {an}=1 be a sequence of real numbers that converges to A. Using only the definition of…

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Q: 3 n° Cos n+ 5n J

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Q: , 2η En=1 3 er

A: Given series is ∑n=1∞ n2nen3. Here, an=n2nen3.

Q: Determine whether the statement is true or false. If E c,7" is convergent, then I c,(-7)" is…

A: Explanation of the answer is as follows

Q: Every increasing monotonic and sequence is convergent

A: given the sequence is increasing monotonic

Q: 1 1+ 2/2' 3/38 1 1 + 1 + ... 5/5 +

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Q: 2n²+L 7 =

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Q: If E Un is absolutely convergent then (un)² is also n=1 n=1 convergent.

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Q: etermine whether the serres Converges 12 Live age or duer 1- onditionally absoutely 3ntl

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Q: hetermine whether the following serfes converge or diverge for the values of p.

A: In the given question we have to check the series such that the series is convergent or divergent.…

Q: If both E Un and E(-un) converges then E Un| n=1 n=1 n=1 is also convergent.

A: It is given that ∑n=1∞un and ∑n=1∞-un converges.

Q: If > an converges, then a converges. n=1 n=1

A: