Use Gauss's trick to determine H(n)=1+5+9+13+...(4n-7)+(4n-3)+(4n+1) I got n(4n+2)/2 is this correct?

Q: Equating the coefficients of corresponding powers of t gives 2/3(13A2 + 2) = 10A2 + 1, (2.200)…

A: 2313A2+2=10A2+1   .....(1)2935A3+10A2=10A3+2A2     ...(2) We need to solve the equations to find the…

Q: n(n+1)(2n+1) 2.Prove k2 = for n > 1. 6. k=1

A:

Q: A group of scientist believes that their new medicine can heal more than 40% of patients. The…

A:

Q: 1. Prove that for any n > 2, n E N, one has (1-)(--)(--) - (-) - n +1 2n

A: I have solved question no. 1 according to policy rule.   To solve q.1, I have used method of…

Q: find the 4th term of (2n^2-3m)^4

A:

Q: If a coin is tossed 100 times, we would expect approximately 50 of the outcomes to be heads. It can…

A:

Q: 4 The value of 2 n=1 3n2 will be + 6n .... .

A: See solution below

Q: n Find the general solution of o ( :) (2)*y(n-i) =0. ata of any nonzero real

A:

Q: [3n+ 2 (-1)A In 3n + 6 n=1

A: Express the alternative series test for convergence. If ∑n=1∞(-1)nan or ∑n=1∞(-1)n+1an converges if…

Q: 4. Since a certain virus has been contained in Wakanda, researchers has proven that it will be…

A: The number of infected citizens, p thousand, after t weeks is given by…

Q: 3. Solve the recurrence hn 5h-1-6hn-2 + 6n – 7, (n 2 2) with ho = 7, h = 11. %3D

A:

Q: n-1 For all n > 2, 4+ 3n4" – 4n+1 - j=1 9.

A:

Q: 3t Q3) Verify that -e-3t e 3t are solution for re-3t 3t 1 e-3t -2 21 2 X on (-0, ∞). 2 X': -2 1 2 1

A:

Q: Use the substitution method to show that the solution of T(n) = 2T(n/3) + n2is O(n2)

A: Given that T(n)=2Tn3+n2 To show that it is O(n2).

Q: Solve T(n) = 6T(n/2) + n^2 using substitution method.

A: The objective is to prove that Tn=2Tn/2+n. Let's guess that the solution is Tn=Onlogn. So it would…

Q: If x1 = 2, xn = 3xm-1 + 2, Vn > 2. Find the general tem æn

A:

Q: 2n [3] (b) E for n 21 2k k=0

A: Answer

Q: The coefficient recursion relation for the solution Y1 = E an x"+1 of the %3D n=0 equation x2y" –…

A:

Q: Show that for any 1 ≤k≤n. T (1) = n²(n²-1²)...(n² (k − 1)²) 1.3.5 (2k-1)

A:

Q: Find the optimum solution for the-3 following modal using the graphical method. Max Z =4X1+3X2…

A: Above question is solved.

Q: By using the iterative formula Xn+1 and xo = O O 0.3652 O 1.3652 O2.6352 = 1.5, then the value of x5…

A: Find the value

Q: use gauss's trick to determine R(n)=2+3+4+...+(n-1)+n+(n+1)

A: It is known that sum of first n numbers is n(n+1)2  that is  1+2+3+----+n=n(n+1)2 Gauss trick method…

Q: (-1)"(п + 2) 2n+1(n +1) Compute the exact value of n=0

A: The geometric series formula is ∑n=0∞rn=11-r, where r<1. Simplify the numerator of the given…

Q: 3 divides n^3 + 2n, whenever n is a positive integer. Solve using mathematical induction

A:

Q: . Show that if an = 3n3 - 17n2 + 2n - 6, then an = Θ(n3).

A:

Q: 2. Let, a1= 3 and for n ≥ 2, an = 2an-1 + 1, express an in terms of n. for n ≥ 3, an = 2an-1+ bn-1…

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS. WE ARE ANSWERING ONLY FIRST QUESTIONS FOR YOU AS…

Q: nx) in the E 2n is

A:

Q: If a_1=9a1​=9 and a_n=4a_{n-1}an​=4an−1​ then find the value of a_5a5

A:

Q: Suppose that a random number  is chosen from the interval (0,2). What is the probability that the…

A: Given: The random number is chosen from the interval (0,2). Quadratic equation is 4x2-x+k

Q: Please help I’m stuck on this one, I’m stuck

A: Introduction: Big-O notation analysis on polynomial function: If f(n)=a0+a1n1+a2n2+...+amnm, then…

Q: 7 45 and fourth term of (3x -) 6. Find the product of expressed 2 as P.

A: The complete solutions are given below

Q: 4+5n Solve for n if nEN: (4+8+12 + ... +4(n –1))+ (2+4.5+7+. .. -%3D126.5 2.

A:

Q: 16. There is a very quick way to compute £-, 2'(-1)ª-' (); do use it. l=D0

A: Introduction: The binomial theorem is very important in mathematics. For any real numbers a,b with…

Q: 10) Which of the following shows the solution for n2 + 2n 2 24? A) 4十 -6-5-4-3-2-10 123456

A: The given inequality is n2+2n≥24

Q: HW Solve the fallowing first order 0E. -3= \-3+メー

A:

Q: If x1=3, ,x2=3, xn=−6xn−1−5xn−2, ∀n≥3x1=3, ,x2=3, xn=−6xn−1−5xn−2, ∀n≥3. Find the general tem xn

A:

Q: (4x +16x² - 44X If-a) is the G.C.D. of ax² + bx+c and ex² + ax + b such that c 0, then prove a + b³…

A:

Q: 2. Σ--1)k , k%3D k+1

A: The given sequence is ∑k=0∞-1kkk+1

Q: Solve for n if nEN: (4+8+12+ ... +4(n-1)) + (2+4.5+7+. .. 4+5n -%3D126.5 2

A: Sum of n natural numbers is n(n+1)/2.

Q: 9. Solve the following equation. sec x - 2 -0 A) 元 x -+ 2n and x- 2n7, where n is an integer 6 B) x…

A: Given: sec x-2=0

Q: (-1)" (n+ 2) 2n+1(n + 1) Compute the exact value of

A:

Q: 4. Theoretically, what is the highest possible value for the slugging average? Could a player ever…

A: Given, the baseball example.     We have to find the highest value for slugging average?

Q: If #1 = 5, ,x2 = 3, an = -4xn-1 + 5xn 2, Vn 2 3. Find the general tem an

A: Characteristic equation is: r2=-4r+5r2+4r-5=0r+5r-1=0r=1,-5

Q: Find the possible values of n. (n2 )" – 2n" + 1 = 0 (n +0,1)

A: We have  n2n-2nn+1=0 and n≠0,1 We can write n2n as n2n=n2n=nn2 So, nn2-2nn+1=0 Let nn=x x2-2x+1=0

Q: 11) Which of the following shows the solution for n2- 2n < 24? 十十 A) 6-54-3-2-10123456 + +++++++…

A:

Q: Solve the recursion by substitution for  T(n)=2T(n/4)+n2 where T(1) =1

A: To solve by putting T(1)=1

Q: 3n – 5n is n→ o n° - 2n² +1 lim 3

A: It is given that, limn→∞3n3-5nn3-2n2+1.We have to evaluate it.

Q: -6an-1 for n > 2 with the initial condition a = -9. an an

A: Given an = -6an-1

Q: 2n2 – 4n +1 is even → n is odd

A: