Show that F0F1 . . . Fn−1 = Fn − 2 for all n ≥ 1, where Fi is the i-th fermat number

Q: Let = n n i=1 x₁ . Then for constants a and b, n Σ a(x₁ - ī) b² =? (6²5m)

A: The question is about parametric inference.Given :Where,X1, X2, ...., Xn are independent random…

Q: c1x1(a) + c2x2(a)+ . . . +cnxn(a) = x(a). Let X (t) be the n x n matrix with column vectors x1, x2,…

A: Given : Xt be any  matrix of n×n           : c be column with component c1 ,c2 , . . .  . . .  ,cn…

Q: Let = e²i/n be an n-th root of unity. Show that (k(1-n) Resck (27²1) n for all 0 <k<n-1. =

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Q: 5) — = [(-D)" (2-1)", when 12-1}<1. n=0

A: Introduction: A geometric series is a type of series which is in the form as follows:…

Q: Prove that if n is a +ive integer,

A: Given that, M xddxnf(x);p = (-1)npnF(p) We can prove this by mathematical induction.

Q: Determine. '{F}. 4s2 + 3 sF(s) – SF(s) – 2F(s) = - s + 4s

A: Rewrite the given equation.

Q: Let n 2 2. Assume that Fn is prime. show that Fn = -1.

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Q: f the population of a certain county was 100,000 in 1998 and 110,517 in 2008 and the for- mula y 5…

A: Given, the population of a certain county was 100,000 in 1998 and 110,517 in 2008             and…

Q: Find the integral

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Q: For all n ≥ 1, let an = (a) Find a1, a2, A3, A4. (b) Computea. i=1 (c) Computea. i=1 (n + 1)² n!…

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Q: determine L−1[F].

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Q: Show that |Z(Dn)|=1 or 2 according to whether n is odd or even

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Q: Q5 Show that EL >². n n =1

A: Consider that x is a random variable. From the formula of population variance;

Q: Prove that πd/n n = nτ(n)/2.

A: your question has a silly mistake, it should be πd|n d = nτ(n)/2. supposeτ(n)=r , where r be the…

Q: Test for vergances of fallowing Cor +oo Σ n=1 Jn² +n

A: Limit comparison test : Suppose we have two series ∑n=1∞ an and ∑n=1∞ bn where an,bn≥0 for all n…

Q: Let A =[1 1        1 0] (in the giant brackets I just don't know how to do that on here) . Show that…

A: Given,A = 1110To show:An= fn+1fnfnfn-1

Q: (1.2) Show that m m+n+1] m k=0 for any two positive integers m and n.

A: Please check the next step for detailed answer.

Q: Let n 2 2. Assume that Fn is prime. show that -1.

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Q: Let A = 21. (a) Compute A², A³, and A4. 02 (b) Find a formula for A" for any integer n ≥ 1?

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Q: Which among the interval whose f(x) is increasing? а. (0,5) b. (-4,0) с. (5,7) d. (-7,-4) e. None of…

A: The function y=fx is an increasing function if x increases then y also increases. that means if we…

Q: (6) L {(1+ te-t)a}.

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Q: Let X N(10, 23). Then P( X< 10) =

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Q: Show that (an) is increasing

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Q: Which of the following statement is always false? (a) For all integer x, [x] = [-x] (b) For all odd…

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Q: T: R³ R², 7(e₁) = (1,3), T(e₂) = (4,2), and 7(e) = (-5, 4), where e₁,e2, e3 are the columns of the 3…

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Q: (b) Pr[X > 0.6n] < 0.85. Let X be the number of HEADS after n fair coin tosses. Show that

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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.