Question

Consider the sequence (xn)n given by x1 = 2, x2 = 2 and xn+1 = 2(xn...

Consider the sequence (xn)n given by x1 = 2, x2 = 2 and xn+1 = 2(xn + xn−1).

(a) Let u, w be the solutions of the equation x 2 −2x−2 = 0, so that x 2 −2x−2 = (x−u)(x−w). Show that u + w = 2 and uw = −2.

(b) Possibly using (a) to aid your calculations, show that xn = u^n + w^n .

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Define a sequence (xn)n≥1 recursively by x1 = 1, x2 = 2, and xn = ((xn−1)+(xn−2))/...
Define a sequence (xn)n≥1 recursively by x1 = 1, x2 = 2, and xn = ((xn−1)+(xn−2))/ 2 for n > 2. Prove that limn→∞ xn = x exists and find its value.
Let n ≥ 2 and x1, x2, ..., xn > 0 be such that x1 +...
Let n ≥ 2 and x1, x2, ..., xn > 0 be such that x1 + x2 + · · · + xn = 1. Prove that √ x1 + √ x2 + · · · + √ xn /√ n − 1 ≤ x1/ √ 1 − x1 + x2/ √ 1 − x2 + · · · + xn/ √ 1 − xn
Consider a sequence defined recursively as X0= 1,X1= 3, and Xn=Xn-1+ 3Xn-2 for n ≥ 2....
Consider a sequence defined recursively as X0= 1,X1= 3, and Xn=Xn-1+ 3Xn-2 for n ≥ 2. Prove that Xn=O(2.4^n) and Xn = Ω(2.3^n). Hint:First, prove by induction that 1/2*(2.3^n) ≤ Xn ≤ 2.8^n for all n ≥ 0 Find claim, base case and inductive step. Please show step and explain all work and details
Let X = ( X1, X2, X3, ,,,, Xn ) is iid, f(x, a, b) =...
Let X = ( X1, X2, X3, ,,,, Xn ) is iid, f(x, a, b) = 1/ab * (x/a)^{(1-b)/b} 0 <= x <= a ,,,,, b < 1 then, Show the density of the statistic T = X(n) is given by FX(n) (x) = n/ab * (x/a)^{n/(b-1}}   for 0 <= x <= a ; otherwise zero. # using the following P (X(n) < x ) = P (X1 < x, X2 < x, ,,,,,,,,, Xn < x ), Then assume...
Define a sequence (xn)n≥1 recursively by x1 = 1 and xn = 1 + 1 /(xn−1)...
Define a sequence (xn)n≥1 recursively by x1 = 1 and xn = 1 + 1 /(xn−1) for n > 0. Prove that limn→∞ xn = x exists and find its value.
If (xn) ∞ to n=1 is a convergent sequence with limn→∞ xn = 0 prove that...
If (xn) ∞ to n=1 is a convergent sequence with limn→∞ xn = 0 prove that lim n→∞ (x1 + x2 + · · · + xn)/ n = 0 .
Let n greater than or equal to 1 be a positive integers, and let X1, X2,.....,...
Let n greater than or equal to 1 be a positive integers, and let X1, X2,....., Xn be closed subsets of R. Show that X1 U X2 U ... Xn is also closed.
Consider n independent variables, {X1, X2, . . . , Xn} uniformly distributed over the unit...
Consider n independent variables, {X1, X2, . . . , Xn} uniformly distributed over the unit interval, (0, 1). Introduce two new random variables, M = max (X1, X2, . . . , Xn) and N = min (X1, X2, . . . , Xn). (A) Find the joint distribution of a pair (M, N). (B) Derive the CDF and density for M. (C) Derive the CDF and density for N. (D) Find moments of first and second order for...
Let X1,X2...Xn be i.i.d. with N(theta, 1) a) find the CR Rao lower-band for the variance...
Let X1,X2...Xn be i.i.d. with N(theta, 1) a) find the CR Rao lower-band for the variance of an unbiased  estimator of theta b)------------------------------------of theta^2 c)-----------------------------------of P(X>0)
) Let α be a fixed positive real number, α > 0. For a sequence {xn},...
) Let α be a fixed positive real number, α > 0. For a sequence {xn}, let x1 > √ α, and define x2, x3, x4, · · · by the following recurrence relation xn+1 = 1 2 xn + α xn (a) Prove that {xn} decreases monotonically (in other words, xn+1 − xn ≤ 0 for all n). (b) Prove that {xn} is bounded from below. (Hint: use proof by induction to show xn > √ α for all...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT