Choose the letters of the sequences that are bounded. {sin(n³}" A. n=1 00 in B. In n=2 C. n=1 D. fne~}. {ne-rt n=1

Q: Find the interval and radius of convergence for: (-1)" k" n=0

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Q: How to prove {sin(n)} is a bounded seuqence that does not converge?

A: To prove xn=sinn is bounded. By definition, a sequence xn is bounded if it is both bounded above and…

Q: Find the limit of the sequence whose terms are given by: a-sub-n = (n^2)(1 - cos(6/n))

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Q: Show that the interval of convergence is (-o, +00).

A: The given question is related with interval of convergence. Given that fx = ex. We have to show that…

Q: Determine whether the sequence 2ñ sin converges or diverges. If it con its limit. 27 1 1 2 diverges

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Q: Find functions defined on the set of nonnegative integers that can be used to define the sequences…

A: For (a), Given: Here, the sequence is f(n)=(-1)n+13n+1 for each n∈ℕ.

Q: Compute the DFT for the sequence [1,1,1,1] x(0)= x(1)= x(2)= x(3)=

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Q: n2 – 1 - at the sequence ɑn is eventually stric n2 + 2 so show that {a,} is bounded above. What can…

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Q: Determine the rate of convergence of the sequence an = sin( as n + 00. A. O(1/n) B. O(n) OC.…

A: given sequence an=sin2n+3n2-5  to find the rate of convergence of sequence as n→∞

Q: {()} Find the rate of convergence of the sequence sin as n=1 n 0 . n n 3 n4 1 n-

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Q: Find the interval of convergence of Σ 6" (2n + 1)!

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Q: the Sequence hver So Lalue. for

A: The given sequence is,

Q: Find the interval of convergence of Σ n=0 (x-7)" n! (Use symbolic notation and fractions where

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Q: Find the point wise limit of the sequence &{fn} the sequence {fr} Where Sin nx In (x) = √n if tay J…

A: Here we use basic limit property

Q: Find sequences (xn) and (yn) so that xn - Yn 0 and yet does not converge to 1 Yn

A: By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: Suppose that anx" converges for x = 5. Must it also converge for x = 4? What about x = -3?

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Q: •(-1)**(x-4)" n9"

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Q: find 1) Taylor’s Formula in powers of (x − x0) that includes the 5-th Taylor reminder, 2) the radius…

A: The given function is fx=1x2-6x+10. The domain for the function is all real numbers. Let's take…

Q: If X1, Y1, are two positive unequal numbers and Xn = (xn– 1+ Yn – 1) and y,= Vx – 1 Yn –1 V n 2 2.…

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Q: Find the interval of convergence of ) n°x" and find its sum. n=1

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Q: п(х — for -1)" n(x – 4)" 2n n3D0 8.

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Q: tx Σ 5 (-1)"(x+3)" n2n n=1

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Q: The sequence {5},-1s: 00 n=1 Converges to 5 O Converges to O Diverges. O Converges to 10 15

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Q: Find center, the radius of convergence and interval of convergence for (-1)k+1 (x – 2)* Σ k k=1

A: The radius of convergence is half of the length of the interval of convergence. If the radius of…

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence…

A: Given query is to find the general term for the sequence.

Q: use SERIES to evaluate the limits

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Q: Find the radius and interval of convergence for (-1)"(x – 1)" n4" n=1

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Q: Show if the sequence converges or diverges using  L'Hôpital's rule…

A: A sequence is said to be converge if its limit  exists, otherwise diverges.L'Hospital rule:- If…

Q: gence for n! n=0

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Q: The sequence whose nth term is given by x_n=sin(n*pi/6) is unbounded is monotonic converges to a…

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Q: Find the radius of convergence for: (6z)" n=1

A: Radius of convergence

Q: Find the radius of convergence for: 5"z" Σ n!

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Q: {sin ()} 2

A: Given sinnπ2

Q: Prove that the sequence is monotone and bounded. Then find its limit. s1 = 5 and sn+1 = V4sn +1 for…

A: See the attachment

Q: Find the interval of convergence of -(x + 10)" n! n=0

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Q: Vn cos(nle") n +1 (n + 1)" (а) ап (b) b, = (c) Cn = 2n sin n nn+1

A: The given sequences area) an=ncosn!enn+1b) bn=(n+1)nnn+1c) cn=2nsinπn

Q: 2. Use the definition to prove that if (xn) is a sequence of real numbers which converges to -3,…

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Q: Find the radius of convergence for: (- 1)"2" n+6 n=1

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Q: Give the raddius of convergence and the interval of convergence for the ( 1)" (nt 1)21

A: ∑n=0∞ x-1nn+12n+1 use the series root test limn→∞|an|1n=L If L<1, then ∑an converges If L>1,…

Q: The interval of convergence of (-b)" x"*1 where b > 0; is n+1

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Q: Find the radius of convergence for EneNZ. n!

A: The given power series is                            ∑n∈ℕnnn!zn We know that if R be the radius of…

Q: is the interval of convergence of the serie

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Q: 8) FIND THE INTERVAL OF CONVERGENCE FOR Σ (-1)" x 1=2 n2^ n

A: The given series: ∑n=2∞-1nxnn2nWe need to find the interval of convergence.

Q: Determine whether the given dliverges. 5. If it sequences converges converges (a) find its Limits•…

A: Given the sequence an = ln n / n arctan(n). We know that, arctan(n) lies in the interval [ -pi/2 ,…

Q: determine convergence by intergral test   sum from 2 to the infinity of 1/n（ln n）^5/4

A: We have given the series

Q: The first term of the mechanic's rule for approximating square roots is a = 1 and it's successive…

A: We have to take limits on both the sides.

Q: (-1)"(n² /n +3) (х-5)" 2" (n° +2) 3 n=1

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Q: Determine the one dimensional DFT for the following sequence x(n)= { 0,\ / 7 / l }

A: Sol:- Given Sequence :- xn=0,1,7,1One Dimension DFT  is given by Xw=11111-j-1j1-11-11j-1-j0171

Q: Find the radius of convergence and the interval of convergence. 2* k=0

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