5. Let a₁ = √5, (a) Find the recursion formula (b) Assuming the sequence converges find its limit 9₂= √5 +4√5, 93= √√5+4√5+4√5,

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A: The main object is to write sequence for given nth term.

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

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A:

Q: 11. (6 points) A sequence is given by the recursive definition bn = 4bn-1, bo = 3. a) Find b₁,b₂,…

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Q: 5n 3) Determine if the sequence a, = converges or diverges. If it converges, find the limit 2n +1…

A: Explanation of the answer is as follows

Q: The limit of the sequence a.- (1+ (a) - (3) e) (c)e None(e)

A: This is 1 to the power infinity form question so accoding to that I wrote the formula to Solve this…

Q: Find the limit of the sequence: 3n² + 3n+6 ап 7n² + 7n +9

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Q: 22: Establish the divergence of the sequence x, =(-1)"

A:

Q: 7. Every sequence of real numbers has a decreasing subsequence. nondecreasing subse- quence or a

A:

Q: 4. Consider the sequence 8 1 {2(k+3 (2(k+3)) k=1 rewrite the sequence from j-5

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Q: The number sequence a1, a2, a3, .... is defined by a1 = 8 a2 = 24 and recursion formula 4an + 1…

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Q: Find the limit of the sequence, or show why it doesn't exist, an = n4-(n8-n5)1/2.

A: Given,  Sequence                     an = n4-(n8-n5)1/2

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A:

Q: Sequence hWith frst tem 7, and las term 7/729.

A:

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A:

Q: 11. Find a closed formula for the sequence with recursive definition an = 2an-1-an-2 with a₁ = 1 and…

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Q: Consider the recursive sequence a ÷(:+*) with a , =3. If I<a,<5 then A. The sequence (a ) is…

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A: the definition of a subsequence of a sequence Xn.

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