4 establish the convergence of dwergence of the following sequences (a) x₁ = 2^²+₁ = x + 1 nti (b) a₁ = 1 a mt 1 Xn 4+зам 3+29m

Q: (f) Assume that g(x) > bna" is convergent on (-R, R). Instead of assuming that f(rn) = 0 assume that…

A: We will prove the part (f) using two theorems   Theorem (a)Let f(x)=∑anxn be a non-constant power…

Q: Consider the sequence aj = 12 a2 = /12 + V12 as = /12+ V12+ Vī2 12 + V12 12 + a4 = 12 + 1/12 + 12 +…

A: a) Given sequence is: a1=12a2=12+12a3=12+12+12...

Q: Determine the interval of convergence for F-)*"(x-2)" 6. Show all your work! n5" n=1

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Q: miformely cari formely Show that Sum of two is Conuergent Convergent. sequence

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Q: Cn an+a2n

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Q: Find convergence radius of sequence  Σ (x^n/n(n+2))

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Q: Please solve it on mat'lab

A: step by step explanation... ### Exercise 5#### a) Sequence an​=(−3)n−1To determine if a_n is…

Q: Petomim whemer mi sunes conmerges If it hnd ti r Conver dhverget. um. -n-2 n² + Tn 12 n=1

A: Check whether the series ∑n=1∞6n2+7n+12+4-n-22n converges or not. If it is convergent, then find the…

Q: (-1)^(n+1)/(sqrt(n)((lnn)^(2)). Prove that those are convergent but not absolutely conve

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Q: -2 (x+6) " is: The radius of convergence of n=1 (-5) "(n)

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Q: lim (1+1)". (a) Define the sequence {bn} by b₁ = 2, and for n ≥ 2, Recall that e lim bn = bn-1 +…

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Q: frind the lower bound for the radius of convergence for (x^2 + 6x−10)y′′+ (x^2 −4)y′+ x^2y= 0 about…

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Q: Discuss the Convergence a 2 e¹ M8 n=1 SH n

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Q: 8. (a) Give an example of a convergent sequence (s) of positive numbers such that lim (s/s) 1. (b)…

A: (Sn​)=(1+n1​) (tn​)=(n)Explanation:

Q: Does the sequences converges or diverges ? A) . (1-)") .«1 +(-1)"), ((-1)". (n+3 2n3 \n+1, n3+1

A: SOLUTION-

Q: . Determine the interval and radius of convergence of (-1)^n² 4n+1 ∞ n=0 -(4x - 2)²

A: The  given equation  is  Now, Then,

Q: Which of the sequences {a,} converge and which diverge: 1. a, = 2+ (0.1)" 2. а, 1+-

A: 1) an=2+0.1n We know that if -1<r<1 then limn→∞rn=0 So, limn→∞0.1n=0 Thus, limn→∞2+0.1n=2+0=2…

Q: Write out the first five terms of the sequence with, [(1 - 7)", determine whether the sequence…

A: To write out the first five terms of the sequence with 1-7n+7nn=1∞, to determine whether the…

Q: Investigate the convergence of: (-1)" (a) 'n + \z|' (b) E (d) n² + \z]' (c) 'n + |z|'

A: Our guidelines we are supposed to answer only first three subparts. Kindly repost other subpart as…

Q: (iv) Σ (−1)n+¹ (n+m)³ • n,mEN Explain here briefly what absolute convergence means for the double…

A: Given: The double sum  mentioned is given by: Where  and  belong to the set of natural…

Q: (b) Analyze the convergence of (-3)" n25n n=1

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Q: Suppose we have the sequence of functions $f_n(x)=x^n$ defined on $[0,1],$ and suppose $f_n\to f$…

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Q: Expand 2z+3 z+1 - in powers of z 1. What is the radius of convergence?

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Q: Determine x(2) if x(n) = (1/3)^ ^(-n). What is the regions of convergence of 2?

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Q: True or false: if (x) converges, then every subsequence (x) is Cauchy. n=] k=1

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Q: Investigate the convergence of: (-1)" (b) (d) (a) 'n + |l° (c) n² + \z]"

A: Infinite series: An infinite series has the form ∑n=1∞ an=a1+a2+a3+a4+…+an+an+1+…,  which means that…

Q: Determine whether each of the following Sequences is convergent. Justify!! @@ (x₁) where x := n 16.…

A: Determine whether each of the following sequences is convergent. Justify.C.   where .

Q: (-1)"n (xn) = п+2

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Q: ax Examine the convergence of , where a>1. x (log xy" +1

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Q: prove by definition 3/n and 1/n^2 converges to 0.

A: We need to prove that two sequences (3/n) and (1/n^2) converge to 0.We need to find that N in the…

Q: (a) Give an example of a convergent sequence (x,) of positive numbers wich lim(x:/x,) = 1. (b) Give…

A: