Write the first 4 terms of the following sequence then determine whether the sequence converges or diverges: {n - Vn +1Vn+3}

Q: n+1 n+1

A: As per the instruction, we will be answering only the first one. For (1),     limn→∞…

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A: The given sequences are a) <an>=n2b)  <an>=2n-1c) <an>=n+1nd) <an>=n+12n…

Q: Q2. Find the general term of the sequence, starting with n=2 and test for convergence.

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A: Given that: 13lnnnn=1∞

Q: n3" converges Determine whether the sequence an or diverges.

A:

Q: 51. аn 2" +3" %3D 4"

A: We have to find the limit of sequence

Q: find a formula for the nth term of the sequence. -1, 1, -1, 1, -1,c

A:

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A: Checking convergence

Q: n+1 –1)' b) An Vn

A: Consider the sequence is, an=-1n+1n3 Then, an=limn→∞1n13=1∞13=0 As n tends to infinity the sequence…

Q: Q: If E find the following: - 2n-1 (n+1)(n+2) 1- The sum of sequence? 2- Determine, if the sequence…

A:

Q: Determine if the sequence converges or diverges: In n n2

A: To check whether a sequence is convergent or divergent first calculate its limit if limit is finite…

Q: 1 (an) = (Vn +1- Vn, ne N. %3D

A: The sequence is:-

Q: Write the first 3 terms of the following sequence, and then find the value they converge to ( or…

A: We plug k=1,2,3 respectively to find the first three terms

Q: b) Decide if the sum converges or diverges. If it converges, find the sum.

A:

Q: Write the terms a1, a2, a3, and a4 of the following sequences. If the sequence appears to converge,…

A: an=10n-1 When n=1, a1=101-1=9 When n=2, a2=102-1=99 When n=3, a3=103-1=999 When n=4, a4=104-1=9999

Q: 3" b) а, 2"+5

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Q: 1. Determine if the sequence converges or diverges and show how you arrived at the conclusion In n…

A:

Q: (-1)"n² n2 + 1

A: Topic: sequence and series

Q: (b) E (n + 1)(n + 2) n=1

A: We have to find

Q: Is the sequence a, convergent or divergent? Exp n+1

A: The given sequence is

Q: Determine whether the sequence converges or diverges 1+(-1)" а. An n2 b. an =(1 -3zn) 3n.

A: For the solution of the problem follow the next steps.

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A: # the given initial value is a1=8 . considering it as t1=8 given the relation tn+1=-2tn+6 substitute…

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Q: Determine if the following sequence converges or diverges. If it converges, state the value it…

A: The solution for the above question is shown below.

Q: th Find the 10 term of the following geometric sequence. 2, 10, 50, 250, ...

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Q: Find the partial sum S, of the arithmetic sequence that satisfies the given conditions. a2 = 9, a5 =…

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Q: 3n Determine if the sequence a, п! converges or diverges

A: Given that: an=3nn!

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A: Determine whether the sequence converges or diverges. If it converges, find the limit.

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A: Given series (i) an=3n+11-2n , (ii) an=(4n+1)3-n , (iii) an=3+(-1)n  and (iv) an=1+(-1)nn4 We have…

Q: Determine whether the sequence convergent or divergent. 3. n =1 n+3 a. diverges b. converges

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Q: Determine whether the sequence converges or diverges n! an (п + 2)! [ Select ]

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

Q: 3n3 – 2n + 1 n² – n3 n=1

A:

Q: Find the partial sum S, of the arithmetic sequence that satisfies the given conditions. a2 = 9, a5 =…

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Q: In(n) An

A: we limit is finite then sequence is converges

Q: The sequence convergent to Answer:

A: The solution is in step 2

Q: i) Determine whether the sequence defined as follows is convergent or divergent: a1 = 1, an+1 = 4…

A: Given: a1=1an+1=4-an          for n≥1

Q: =(-1) 你十2

A:

Q: Determine if each of the sequences converges or diverges. If it converges, state to what. Clearly…

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Q: The sequence (a,) = 2 converges to -2.

A: Let (an) be a sequence. If limn→∞an = L, where L is finite Then the sequence converges, otherwise it…

Q: Determine whether the sequence [In(k²-5)] 3k +4 00 k=1 converges or diverges.

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.