2. The first term of the sequence is r1 = cos(1). The next term is larger; and x3 = x2 or cos(3), whichever is larger. in gen In+1 = max{xn, cos(n + 1) Check the convergence or divergence of the sequence

Q: 3. n-3n+5 n7 Sn=1

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Q: The series C„(x +3)" converges at a = 2 and diverges at x = -12. Based on this information, what can…

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Q: Find the interval of convergence of the series. (3x)" 2" n=1

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Q: If a geometric series converges to a / (1-r) if |r| < 1, the interval of convergence is

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A:

Q: (2 2 First find the sum of this Series: (-1)"b)" the valnes of x for which the given series…

A: ∑n=1∞-1n x-1n3n=∑n=1∞-1nx-13n=∑n=1∞13-x3nFirst term (a) =13-x3,  common ratio (d)=13-x3Sum of the…

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A:

Q: Let fn(x) be the following sequence (not series) of functions n2 fn(x) = (x2 + 7x + 6)n² +n

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Q: Show that the series n" n' is convergent. Deduce that lim (2n)! (2n)! n=1

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Q: Suppose that the power series ) Cn(x – 1)" converges when x = -2 and diverges when n=0 x = 6. (a)…

A: The power series ∑n=0∞cnx-1n converges when x = -2 and diverges when x = 6. We have to find the…

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A:

Q: Find the limit inferior and limit superior of the sequence {[5 sin n]}.

A: The given problem is to find the limit inferior and the limit superior for the given sequence of {[5…

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Q: 8. 3. Use two different methods to show that the series 1 converges. 1+ n2 n=1

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Q: 1) Use the rigorous definition of convergence (in other words, an epsilon argument) to prove that…

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Q: Show that the series 71 n' (2n)! is convergent. Deduce that lim 0% (2n)! n=1

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A:

Q: 2. Consider that > (x – 2)* is a geometric series. As such, for what values of x will this infinite…

A: Given that ∑k=0∞x-2kTo find : Value of xSolution :∑k=0∞x-2kRatio test ak=x-2k…

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A:

Q: Find the interval of convergence of the series k(x+ 2)* 5k+1 k=1

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Q: Find the limit of the sequence whose terms are given by 4.9 1 Cos In =

A: Let's find.

Q: Q2. Check the convergence of the series 2 tan-1 n=1

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Q: х The terms of the sequence defined by al = x and a, for n>1 give successively better An-1 ал-1…

A: a1 = x; x = 2

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Q: 00 n³n² COS 5n³ +3, 1

A: See the answer below

Q: 701 Discuss the convergence of the given sequence: a(n) = sin- 2

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A: Given series: ∑Cnx+6n converges at x=-3 and diverges at x=-12

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Q: 8.1 Define what it means for a series E an %3D to converge.

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Q: Show that the series n" (2n)! is convergent. Deduce that lim 0. (2n)! n=1

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.