2. Use the contraction mapping principle to show that on [1, 2], the equation x-x-1=0 has a unique solution. Construct a sequence in [1, 2] that converges to the solution.

Q: Write out the first five terms of the sequence (-1)" n2 , determine whether the sequence n=1…

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Q: Prove that the sequence ((-1)")=1 does not converge to any number.

A: Solution :- The given sequence is                          {  an }   =   { (-1)n}  then , we have to…

Q: 1) Determine whether the sequence ɑn = find the limit. (2) Hint: Ei = + converges or diverges. If it…

A: Ero mlm gg

Q: Suppose that the sequence x0, x₁, x2... is defined by x = 6, x₁ = 3, and xk+2 = 2xk+1+3xk for k≥0.…

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

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Q: compute the 9-th convergent to √29.

A: We need to find the smallest positive integer solution to  or compute the  convergent to .We will…

Q: Suppose that the sequence x0, x1, x2... is defined by xo=4, x₁ = 6, and xk+2 = 4xk for k20. Find a…

A: Given Data: Let us consider the given data, xk+2 =4xk which can be written as, xk+2 -4xk=0with x0=4…

Q: Define a sequence of ordered pairs (x;, y;) as follows: (xo, Yo) = (3,1) %3D Xn+1 = 3xn + 4yn, n > 0…

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Q: Is the sequence (N SIN N) properly divergent Is the limit +∞ or -∞0 ?

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Q: uppose that the sequence x0, x1, x2... is defined by xo = 3, x₁ =0, x₂=5, and xk+3 = 13xk+1+12x for…

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Q: Does the sequence {a,} converge or diverge? Find the limit if the sequence is convergent. 5/n an

A: The given sequence is an=5n5/n If limn→∞ an exists and it is finite then sequence an is convergent…