Sequence is defined by 02 U。く2 n70: Un = V2- Un-1 Suppose: Po-Von and an= = Uzn+1 * Prove that the Sequene e (Un) bounded com pare Pri Pn and an to 1 .

Q: Let A = {4n^2 + 1|n ∈ Z}. Show that A is a subset of Z but not equal.

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Q: Let yk = k", where n is a positive integer; then Ak" = (k + 1)" – k" - (1.112) nk"-+ n kn-2 +...+ 2.…

A: We have to solve given problem:

Q: How 3 used a (aluchy - Schwarz invquality Fuclideran distance. the to show that matric on R"

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Q: Suppose f"(x) = N;(h) + a,h* + a;h® + azh® + ... When calculating N,(h) using Richardson…

A: Solution

Q: 1. 15x4- 13x²+ a is o(x*) . Hint: Apply theurem I.

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 6.) Derike the binomial idendity nent) (un-) C Hint: For mzz, c^)+2(^) +m?]

A: To derive the binomial identity22+42+62+.........+2n2=nn+14n-16

Q: Let f and g be permutations. Show that the order of h=fgf^−1 is the same as the order of g.

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Q: Prove that lor n {k=1 positive unteger every K2K = (n-1)2²+¹+2

A: answer is in next step.

Q: Give a recursive definition with initial condition(s). a) The function f(n) = 5", n = 0, 1, 2, ....…

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A: Here we will use the ratio test for convergence of series

Q: n=1 35. Suppose x is an accumulation point of {a,:n E J}. Show that there is a subsequence of {a,}=1…

A: We need to show that there is a subsequence which converges to x

Q: If the given three vectors are coplanar, then find the value of x. A = i-2j + 3k, B = xj + 3k, C =…

A: A, B, C are coplanar.So

Q: 5. Find A-1 and A4 if 3 0 0 0 0-1 -1 0 0 A = 0 0 1/2 0 .0 00 1

A: 5. Given that the matrix is                                To find

Q: B3.3.4.1f) (1) Use limit laws and SL. 1 - SL. 8 for sequences, to evaluate the following limits: cos…

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Q: 1) Consider the arithmetic mean (x +y)/2 and the geometric mean xy of two positive numbers x and y.…

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Q: 1. てー d Sinlt).losl). 1-(-1)2 ー1 1. Suppore an an dao 十} an and a, =2." Show that 9nt! the Sequence…

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.