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1. Use mathematical induction to prove that 2-2*7+2*7^2-.....+2(-7)^n=(1-(-7)^n+1)/4 whenever n is a nonnegative integer.
2. Show that 1^3+2^2+....n^3=[n(n+1)/2]^2 whenever n is a positive integer.
3. Use mathematical induction to show that 3 divides n^3+2n whenever n is a nonnegative integer.
Write the generator matrix. Show by example that your code will detect 1 error, 2 errors, and 3 errors. Give an example where 4 errors are made in transmitting a message word, but your code does not detect any errors.
The included angle of the two sides of contant equal length s of an isosceles triangle is Z degrees. Show that the area of the triangle is given by A = 1/2s^2 sin Z
Compute the inverse of matrix A below, and use this to express A as a product of elementary matrices
Solve for the Boundary Value Write a solution of the boundary value problem. 2u/2t = 4(2^2u)/(2^2x) for 0 0
Compare this to the actual value of the derivative and compute the percent error for each approximation
Suppose that f is continuous on [a,b], f(z) 0. Set z = sup{x: f (t)
Let (S,d) be a metric space and define the function u(x,y) = d(x,y)/(1+d(x,y)) for all x,y
Step by step process in solving the following question. Using matrix algebra techniques, find a general solution of the system:
Either explain why f is not linear or write down the matrix that represents f . iI general how do you solve problems of this type?
Solving probability problems based on Binomial distribution
Important information about Probability and Expected Value. Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability that the second marble is blue, given that the firs..
Prove that the subgroup of A4 generated by any element of order 2 and and any element of order 3 is all of A4. Prove that if x and y are distinct 3-cycles in S4 with x != y^-1 (x not equal to the inverse of y), then the subgroup of S4 generated by x..
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