Mark each sequence {n} having the property that In In (-1)"n n+1 In |xn = (-1)" In = {cos(nn/3)} 1 when n is odd, and ™₂ = 1 + when no is even. n lim sup n

Q: What is the closed form for the infinite geometric sequence beginning  4,2,1,1/2 where the first…

A: Given :The infinite geometric sequence : 4, 2, 1, 12, ..

Q: Define a sequence (Sn)n inductively by letting S1 = 1, and Sn+1 = Sn + 1. 1+V5 Prove that lim Sn = .…

A: Limit of a sn

Q: 25) Show that the sequence (2/7) n! 10") +∞ n=1 is eventually strictly decreasi

A: The given sequence is: {10nn!}n=1+∞ which is to be shown as decreasing. First, we shall know the…

Q: Find lim,00 sup(sn) and lim,→0 inf(sn) for the sequence: 82n = (-1)"(n); s2n-1= e7 = et

A: The sequence is S2n=-1nn. Find limn→∞sups2n and limn→∞infs2n: Consider and obtain the limits:…

Q: Is the sequence {cos (-)- In(n)}, monotone? If so is it increasing creasing? or de-

A:

Q: PIUVE thlat Un 2 X9. A sequence {an} is defined recursively by ao = 1, a1 = 2, a2 = 24, and an = n 2…

A: The recursive relation has been proved in step 2.

Q: Use the difference an+1 – an to show that the sequence {n – 11"}t n=1 is strictly increasing or…

A:

Q: Suppose that the sequence x, x1, x2... is defined by xo-1, x₁ =6, and xk+2=7xk+1-12x for 20. Find a…

A: Ans :

Q: a,=(- 1)" is a divergent sequence

A:

Q: 3. Show that the sequence is convergent or divergent by definition: n² + 1 2n² - n an = (-1)" + =-,…

A:

Q: Determine lim an for each sequence (a,} If the limit doesn't exist, explain why. 4n2 • a. an %3D 2n3…

A:

Q: Q\ Find the infimum and supremum of the sequence (a„)nen = (n(1 +(-1)") + n='((-1)" – 1). nƐN

A:

Q: Find a closed form solution for the following recursive sequence: An 3an-1+2 for n > 2 with the…

A:

Q: Use the difference anti-an, to show that the given sequence {a} is strictly increasing or strictly…

A:

Q: 8. Consider the sequence {an} such that an+1 = -3 – 2an. Then lim an = -1.

A:

Q: Find a closed form solution for the following recursive sequence: An = an-1+ 2" for n > 2 with the…

A:

Q: an = (-1)", bn Cn = n² dn= n (a) For each sequence, give an example of a monotone subsequence. 6n +…

A:

Q: 2n + 3 Which of the following is true about the sequence (a,) where a, = 5n + 4 (a) lim a, = +oo (b)…

A: Given that; an=2n+35n+4

Q: What is the formula for the nth term tn of the folowing sequence tn = -4 + tn-1 when t3 = pi/6,…

A: Given tn= -4+tn-1  ---(1)and    t3 = π6

Q: A sequence is defined by f(1) = 3 and f(n) = 2. f(n –1) for n > 1. Which of the following statements…

A: Here given  f1=3,fn=2·fn-1

Q: Let an be a sequence defined by a1 = 0 and a2 = 1 and for n > 3 an = (n – 1)(an-1+an-2). %3D

A: Here, the terms given in the series are, a1=0,a2=1an=n-1an-1+an-2 Calculate the third, forth and…

Q: Which of the following sequence is divergent? en {"} (-1)*+1 n s n² In+1 } {-3}

A:

Q: 5. Find the 6th term of the recursive sequence defined by a₁ = 0, an+1=2a₁ +3.

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Q: how that the sequence (1 – (-1)" +1/n) is divergen

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Q: In 3n an = In 5n

A:

Q: Indicate a general rule for the nth term of the sequence when a, = 2 and r = a, = (/2)(5y* a, =…

A: Given query is to find the nth term of the sequence.

Q: Define a sequence (Sn)n inductively by letting S1 = 1, and Sn+1 = Sn + 1. 1+V5 Prove that lim S, = 2…

A:

Q: Consider the sequence defined by a_n= (4n + (-1)^n2 - 2)/8 for every integer n > 0. Find an…

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Q: 1 Decide whether the sequence an converges and if so, calculate limno An : 3n - 2n 4n an

A: To decide whether the sequence  converges and if so, to calculate .

Q: a. the sequence is given by an=1/(n^7/6)      lim n→∞ an=  b.  the sequence is given by…

A: We need to solve separately a. the sequence is given by an=1/(n^7/6)      lim n→∞ an=  b.  the…

Q: Given the sequence 41, 4.4 what is f(n)? 4+ f(n)=4+ f(n)=n+ f(n)-5-- 4+n 1 4+n n

A: We rae required to find the general term of the given sequence.

Q: Consider the sequence recursively defined by bị = 3, b2 4, and bn+1 2b, + bn-1 for n > 2. Show that…

A:

Q: 9.) Define what is the sequence {Xn} diverges n = ∞ as meant by to +00/-00

A: A sequence {xn} diverges to +∞ as n approaches infinity, it means that the terms of the sequence…

Q: converges

A: