4. Let bo = 1, b1 = 3, and for cach integer k> 2, we have bz = 4bg–1 - 4bg-2 Prove that for all integers n>0 we have that bn = 2" (1 + 5) %3D

Q: 16-17. Find the value of n that makes AFED~ AZYX when DE = 4, EF = 5, XY = 4(n + 1), YZ = 7n – 1,…

A: To find the value on n so that two given triangles becomes similar.

Q: Based on Theorem 4.4.3 P.169, when n > 2, which of the following is biggest? 1. n! 2. n^n 3. (n!)^2…

A: We have to find biggest number among of them

Q: 6.8 Obtain a test for Ho: B1 = c versL

A:

Q: Also, from Theorem 4.9', we have k2k-1 k2k [(E – 2)(E – 1)(E +2)]¬!2* (4.239a) (1 · 4)(1!)…

A: The one is red is [(E-2)(E-1)(E+2)]-12k=k2k-1(1*4)(1!)=k2k8        (1)y(P)k=-79k-k26+k2k8…

Q: Consider a, = V4n² + 3n – 2n for n > 1. %3D -

A: Introduction: The sequence is a set of functions with the set of natural numbers as the domain of…

Q: If (ar + br) 4n and n+1 k-1 E(ak - br) 1 then ar = | n+2 k-1 k-1 3 5. None 2. 72n/2

A: use elimination method Find limit for n tending to infinity.

Q: 10. Use Euler's method, starting at x computations that lead to your ar 1.2 1.3 1.4 10 12 13 14.5

A:

Q: GIVEN: xihl i+ 2) 드 hai (-1)" (n + 2) 2"+1(n + 1) 4. Compute the exact value of n=0

A:

Q: If n^2+6n+11 = x^2+y^2 for positive integer n, x and y prove [xy/2] is composite. Note: [t]…

A: Given :              n2+6n+11 = x2+y2              t ≤ t

Q: If (ar + br) = 2n %3! n+1 and k-1 8. E(ak - br) = n+2 - , then ar %3D k-1 k-1

A:

Q: 3. Prove the Archimedean Property, if x ER. then there exists K E N such that r SK.

A:

Q: If x, y, z are integer's numbers and if x \y then x \ z then: 1) Show that x\ ym – zn for m,n e Z 2)…

A:

Q: 1. Given s=6x720: Find a) whure y is at eauilibriuma is increosing <) whe y is docieosing 5) where

A: Given y'=6x2+7x-20 So, equilibrium of y will exist where y'=0…

Q: 3. Given n > 1, let S = E-1: Show that S, is not k=1 _k° an integer.

A: We are given that   Sn = ∑k=1n1/k   and n&gt;1              ..(i) We have to show that Sn  is not an…

Q: If (n + 1)(n + 2)an+1x" - nan-1x" = 0, n=1 show that for k = 1, 2, 3, ..., we have 1.3.5... (2k - 1)…

A:

Q: 1 О. 15 Show that %3D (D - Q) k e k

A:

Q: Given: In(1+x) = >) (-1)". -xn+1 if |x| < 1. n+1 n=0 Compute the exact value of -1)"(n+2) 2n+1(n +…

A: Given: ln(1+x)=∑n=0∞(-1)nn+1xn+1 where x&lt;1To Compute: Exact value of ∑n=0∞(-1)n(n+2)2n+1(n+1)

Q: 1- Two vecters n'and mª anl Said to be orthogenal if n'entzo T b. F a.

A: The given statement is: Two vectors n and m are said to be orthogonal if nxm=0 To determine whether…

Q: (7) 13. Find two positive numbers, z and y, such that their product is 500, and z +3y is as small as…

A: Topic: calculus

Q: 1. Find homogenous solution of the following rule. 2. Find complementary solution of x (Xp) using I

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: (8.20 ds: Find the tayLor seri's expen sian of In Cxri) about XozO

A:

Q: Q4) • l'ren that nny nesorintive binnry operation defined onA s with two eleinents is emnmstatiw.

A: Let a non-empty set A. let a, b∈A. Now we define a binary operation  a*b=b Now associative property:…

Q: Problem 19.1. Prove that 2019 can not be represented as a sum of three fourth powers o integers…

A: Take the fourth power of integers from 1 to 7 and obtain that 74 is greater than 2019. Therefore, to…

Q: 1 -dr. a In r| Find 3.

A: Let's find.

Q: If Pn: 49^n +16^n + k is divisible by 64 for all natural numbers is true, then the least negative…

A:

Q: a n eln t--+

A: Given a function : h(x)=31-2x+2 We need to find the graph of this function.

Q: 4) We know that () and a!=1.2...a. Prove that Yn75, )< 2n-2. G0od Luck!

A: Given, ab=a!(a-b)!b! and a!=1.2....a

Q: ) A certain appliance is designed to operate at no less than 9/2% below its nameplate voltage and at…

A: Given: A certain appliance is designed to operate at no less than 9/2% below its nameplate voltage…

Q: Suppose we observe X1, X2, ..., X U (0, 1). Show that nX(1) 4 Exp(1). с.

A:

Q: that for n > k we Sn+1 ||

A: The expression given is ,  n+1k+1=∑j=knnn-jjk The number of ways to partition n+1 objects into k+1…

Q: Let s: = ∑_(k-1)^(n=0)rk. Compute s(1-r) = s - rs, and solve for s. Then prove r ≠ 1, for…

A: We need to prove that the sum S= (1-rn)/(1-r) when r is not equals to 1.

Q: Prove the following: 1) 1+3+5...+ (2n-1) = n²

A: *By Bartleby policy I have to solve only first one as these are all unrelated  problems.These are…

Q: Prove for r ≠ 1 that ∑_(k=0)^(n-1)(rk)=(1-rn)/(1-r). If ∑_(k=0)^(n-1)(rk), then compute s(1−r) =…

A:

Q: If (ar + br) : 8n and n+1 %3D k-1 (ak - br) +, then E ak = n+2 k-1 k-1 None 2.

A:

Q: Prove that (0.01)(100sin2π(5000)t)2 is equal to 0.5+0.5cos2π(10000)t

A:

Q: 1. Show that for all z1, Z2 E C, Then we have: |Z1 + z2| < ]z1]+ |z2| 2. Show that for all z1, Z2 E…

A:

Q: 15. prove that L. d= nd(n)/2

A:

Q: 1. For an = 5n2 + 9n3 + 1, an = n2, prove or disprove: rn = O(an) (n → o)?

A: We will use the standard definition.

Q: = o sdue the second solution of the Qifferentiol equotion with the help of Abel formula yu-27y'+d'y=

A:

Q: For xn = 5n² + 9n³ + 1, an = en = n², prove or disprove: an = O(an) (n → 0)?

A:

Q: Show that for any n E N, n(n + 1)(2n + 1) %3D k=0

A:

Q: 2+13 Evaluate zdz along the following paths- (a) horizontally from 1 +i2 to 2+ i2 then vertically to…

A:

Q: . Let, a, = 1, az = 2, b; = 0, b2 = 1, for n2 3, a, = 2an-1 + bn-1 for n22 b, = br-1+ an-1 express…

A:

Q: 6. Given that -뿔 (금) (규 R(x) 4! 1+. for x E (-, 3), where & is between x and 0, find an upper bound…

A:

Q: If det A= 0 why is det A+ = O? If A has rank r, why does A+ have rank r?

A: Given Data det A=0   Suppose the column and row of the matrix are linearly independent. The matrix…

Q: 8. Working over R, suppose that M = PDP ' where P 1 Then, for any positive integer k, we have that…

A: To find Mk =?

Q: 4- Prove Sca) < ela) and Conclude if ea is la-ea small Compared to lal then: ela) S(a) lal

A:

Q: 6n_ and If (ar + bx) = n+1 k-1 , then 1 (ak – br) = 712 n+2 k-1 k-1

A: If ∑k=1nak+bk=6nn+1 .......................(1)  and  ∑k=1nak-bk=nn+2-1n ......................(2) we…