2. For each of the following statements • Write down a roadmap for a proof of it by induction. • Fill in the details of your roadmap to prove the statement. (i) n! < n" for all n e N. 1 (ii) m3" > 100 × 2" for all n € N with n > 23. [You may use a calculator 100 for the base case. - 6ak Define the sequence (ak)kEN by a1 = 2, a2 = 5 and ak+2 = for all k > 1. Then an = 2"-1 +3"-1 for all n > 1. 11 5ak+1 %3D

Q: I need help with linear transformation as I am confused what to do with the circle or angles. I have...

A:

Q: Find T(v) by using (a) the standard matrix and (b) the matrix relative to B and B'. T: R² → R³, T(x,...

A:

Q: Kindly .. Find the degree of homogeneity for the following function:

A:

Q: Convert 4 digits to binary and hexadecimal? Numbers: (0315)

A:

Q: Problem. 12.1 : Write the equation of the surface in rectangular coordinates. x^2/9+y^2/4

A: According to our norms we can't give solution to every question.If you want solution of the rest que...

Q: Thank you for your assistance

A:

Q: 4. The table below shows the number, in thousands, of vehicles parked in the central business distri...

A: As per our guidelines, we can answer only three sub-parts in a session. Please re-post the remaining...

Q: Find Laplace transform of the function

A:

Q: (cos 2a) y/" – y = 0; y (0) = 1, y (0) = 1

A:

Q: The ratio Fib(n+1) /Fib(n) as n gets larger is said to approach the Golden ratio, which is approxima...

A:

Q: Suppose that, in a divide-and-conquer algorithm, we always divide aninstance of size n of a problem ...

A:

Q: Graph the curve traced by the given vector function r(t)=ti +2tj+costk;t>0.

A:

Q: Let A be a 2 x 2 matrix. a) Is it true that if A is diagonalizable then A must be invertible? If so,...

A:

Q: 1 dt, for x > 4. In(t) Let F(x) 4

A:

Q: A crane lifts a block from ground level at a constant speed. After 5s the block slips from its shack...

A:

Q: 4. Convert the integral to spherical coordinates and evaluate the integral. V49 - x? s V49- x² – y² ...

A: Given integral is ∫07∫049-x2∫049-x2-y2x2+y2+z2dzdydx We have to convert it to spherical coordinates....

Q: 14 - BIU 343.4 +5.607%3D 800.54 + 90.52%3D 809.144 15.963D 94.9 41.871%3D 767.3 24.9 = 803.309 133.3...

A: This is addition and substraction of two numbers.  

Q: Problem 2: Three surveyors have placed themselves at three locations around the edge of a canyon and...

A:

Q: Rewrite the given expression using a single power series whose general term involves xk.

A: Concept:

Q: Consider the intergral of(2x + 1) dx from 1 to 5Estimate its value using 4 and 8 subdivisions of(i) ...

A: Note:- In given problem, you don't mention Simpson Rule name (Simpson 1/3 Rule or 3/8 Rule). Due to ...

Q: Find the solution to the following initial value problem using Laplace Trans- form: x" + 9x' + 14r =...

A:

Q: 15.4 5

A:

Q: (c) Let ɛ be a number so that 1 > e > 0. Explain why the integrals dx, dx x2 -1 can be computed usin...

A: For (c), Let ε be a number so that 1&gt;ε&gt;0. Now, we will show why ∫ε11x2dx,   ∫-1-ε1x2dx can be ...

Q: Find the solution to the following recurrence relation: An = 2a,-1 for n > 2 with the initial condit...

A:

Q: state clearly what answer is and box it

A: The given equation is tanθ=9. Find all angles θ that lie between 0° and 180° satisfying the equation...

Q: Find the future value of an ordinary annuity of $4,000 paid quarterly for 4 years, if the interest r...

A:

Q: A function and its first and second derivatives are given. Use these to find each of the following. ...

A: Given that, the function is fx=27x-223x2 "It is known that, If the polynomial in the numerator is a ...

Q: 14. Find the eigenvalues and bases for the eigenspaces of 425 for -1 -2 -2 A= 2 1 -1 -1

A: If a is eigenvalue of matrix A then ak is an eigenvalue of matrix Ak.

Q: Q) S = the part of the paraboloid z = 10-x^2-y^2 above z = 1 F = [x^3, xy, z] Find the flux of F acr...

A: The vector field is F→=x3, xy, z. Given: S = the part of the paraboloid z=10-x2-y2 above z=1. The fl...

Q: 2. Find all solutions of the linear congruence 12x = 9 (mod 15).

A: P

Q: The function f(x,y) = 3x2 - 2xy + y2 + 8y has one stationary point. What is the location and discrim...

A:

Q: A market analysis employed by the "Sad Student Company" reveals that the number of lots of the game ...

A: Given,            p = 1500 - 2.5q

Q: Verify that y(t) = ceat solves the differential equation for unlimited growth, y' = ay, with initial...

A:

Q: calc 3 Change from rectangular to spherical coordinates.

A: we have given in rectangular coordinates and have to convert in spherical 

Q: Part B

A: Pointwise convergent:- A sequence of function is pointwise convergent, if its every point sequence i...

Q: Write the sum using sigma notation: 1+ 2+3+4+.+ 129 > B, where ... n=1 A В

A:

Q: The sales of a book publication are expected to grow according to the functionS = 300000(1 − e-0.06t...

A: Given that, the sales of a book publication are expected to grow according to the function, S=300,00...

Q: Find the partial sum S16 for the arithmetic sequence with a = 7, d = 7. S16

A: Given that, the value of a=7, d=7 and n=16. "It is known that, the formula for the sum of first n te...

Q: 1 -3 -2 Let A = -1 3 1 -4 be a transformation matrix. 3 -9 -5 ) Use Gauss-Jordan elimination to find...

A: Concept: Since rank-nullity theorem is Rank(A) + Nullity(A)= n Where n is total number of columns of...

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.