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Q: If ∑x_n and ∑y_n are convergent, show that ∑(x_n + y_n) is convergent.

A: The objective of this question is to prove that if the series of x_n and y_n are convergent, then…

Q: 3 3) The Sequence of real function f(x) = x²+³ converges over a interval [1,1], dotally from th…

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Q: What is the convergency interval of (-1)"-_(*-2)* 3-(2n+1) {(-)

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Q: 11 +4 Perform a test to determine if Tx converges. 1 11 X' + 4 Does T converge or diverge? 9 1…

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Q: 1. (x² + 1)² dr

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Q: (-1)" Determine whether E1 converges absolutely, converges conditionally or stify your answer by…

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Q: Determine whether converges or diverges. If it converges, compute the limit. (n +1)2 n=0 n+47…

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Q: xp Vx(x + 5) converges O diverges

A: CONVERGES

Q: (X + 2)" 2) Find the interval of convergence for N! N

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Q: 1² + 11 For what value(s) of n, the integral dr converges? Justify In + 8x2 + 2 your answer.

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Q: Determine if the sequence converges or diverges. Briefly justify! When she converges provide her…

A: find the limit of given sequence at infinity.

Q: V2+cos (n2+1) Use the basic comparison test to determine whether E1 n=D1 converges or n+en diverges.

A: To check the Convergency of the given series. We apply here Simple comparison Test and Ratio Test of…

Q: 1 3 .5 4 X +x

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Q: 00 4" converges or diverges. (9n)2 t) Use the ratio test to determine whether> n=6 d the ratio of…

A: We have to use Ratio Test first.

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

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Q: Identify two subsequences of ((−1)^n + 1/n) which converge to different limits. You should include…

A: Let the given sequence is Sn=-1n+1n We have to find two subsequences of given sequence that converge…

Q: 3. Parts of this problem are not related [3] (a) Find the limit of the sequence an = In(10n - 6) -…

A: The limit of a sequence with nth term an is given by the equation; L=limn→∞an

Q: e-Xdx converges xpx

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Q: 4n2 Determine if the sequence {an}I with an= converges. If it converges write its limite if it…

A: Given Data The sequence formula an is:     The expression for the limit of sequence an is,

Q: (6) Show that the sequence {n} with 1 > 0, n+1 = 2+In its limit. n> 1 is convergent. Find

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Q: 3- a- By definition show that (x,) = (+3) converges to 3. b- Does (+3) bounded, Cauchy? Show by part…

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Q: If akxk converges for x = -8, then which of the k=0 following must be true? I. ax* converges for x =…

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Q: Need help with this question. Please explain each step and neatly type up. Thank you :)

A: start with a single vertex v and initialize a trivial circuit CFind vertices in C with remaining…

Q: If it converges, what is its limit? Provide some justification for your answer. If it diverges,…

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

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Q: 8 6. Use the Root Test to determine whether Σ k=1 6k² 2k² +4 k converges absolutely or diverges.

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Q: The series 2n +2 Diverges to-o0 Converges to 1- Converges to B Diverges to +

A: Given series is ∑n=1∞sinπ2n-sinπ2n+2 The Nth partial sum of given series is…

Q: n² +1 rove that the sequence {an},n=1 converges by following the following sequence of steps. n n=1…

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Q: (a) Find a convergent subsequence of the sequence (an) defind by an = (-1)" + 5n 3n+1

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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.