A positive integer n is split into x equal parts, which are then multiplied together. Suppose n 8. Then: xParts Product (approx) 8 16 18.962962 16 10.48576 5.618655 2.5465 4*4 3(8/3) (8/3) (8/3)...
Prove using mathematical induction that for every positive integer n, = 1/i(i+1) = n/n+1. 2) Suppose r is a real number other than 1. Prove using mathematical induction that for every nonnegative integer n, = 1-r^n+1/1-r. 3) Prove using mathematical induction that for every nonnegative integer n, 1 + i+i! = (n+1)!. 4) Prove using mathematical induction that for every integer n>4, n!>2^n. 5) Prove using mathematical induction that for every positive integer n, 7 + 5 + 3 +.......
16: Problem 8 Previous Problem ListNext 1 point) 1) Suppose that f(x) is a function that is positive and decreasing. Recall that by the integral test: f(z) dz < Σ f(n) Recall that e-Σ. ,,Suppose that tor each positive integer k f(k)- Find an upper bound Bor f(z) dz 2) A function is given by ts values may be found in tables. Make the change of variables y In(4) to express 1-4 d as a constant C times h(3). Find...
Let n be a positive integer consisting of up to 8 digits. d8, d7, …..d1.Write a complete C program by usiang a function, to list in one column each of the digits in number n. The right most digit, d1, should be listed at the top of the column. Hint: If If n is 3,407, what is the value of the digit when computed by using digit=n%10; You can test your program for values of n equal to 172,459. So...
4. Let n be a positive integer with n > 20, and let S (1,2.. n21 with IS- (a) Show that S possesses two different 3-element subsets, the sums of whose elements are equal b) Show that S possesses two disjoint subsets, the sums of whose elements are equal.
4. Let n be a positive integer with n > 20, and let S (1,2.. n21 with IS- (a) Show that S possesses two different 3-element subsets, the sums of whose...
,n2} with ISI = n. 4. Let n be a positive integer with n > 20, and let S {1, 2, -I with a) Show that S possesses two dilferent 3-element subsets, the sums of whose elements are equal. (b) Show that S possesses two disjoint subsets, the sums of whose elements are equal
,n2} with ISI = n. 4. Let n be a positive integer with n > 20, and let S {1, 2, -I with a) Show that...
Suppose that nx) 2x3-3x-X+ 2. Using only the theorem on bounds, find the smallest positive integer that is an upper bound for the zeros of f(x) and find the largest negative integer that is a lower bound for the zeros of fx). Upper bound 2, lower bound -2 Upper bound 1, lower bound -2 Upper bound 2, Lower bound 1 Upper bound 3, Lower bound -2 Upper bound = 3, Lower bound #-2 Question 8 (10 points) Find all the...
8. Let n be a positive integer. The n-th cyclotomic polynomial Ф,a(z) E Z[2] is defined recursively in the following way: 1. Ф1(x)-x-1. 2. If n > 1, then Фп(x)- , (where in the product in the denomina- tor, d runs through all divisors of n less than n). . A. Calculate Ф2(x), Ф4(x) and Ф8(z): . B. n(x) is the minimal polynomial for the primitive n-th root of unity over Q. Let f(x) = "8-1 E Q[a] and ω...
Question 4 16 marks Let Y N(Hy, o). Then X := exp(Y) is said to be lognormally distributed with p.d.f. (In(x)-Hy) exp 202 fx(x) TOYV27 and denoted as LN(Hy, of). Let Xı,... , X, be random samples from the LN(Hy,of) distribution (a) Find the maximum likelihood estimator for ty, which we denote as fty (Hint: Use the fact that Yi In(X) is normally distributed with known mean and variance) Verify that the sought stationary point is a maximum (b) Verify...
find and draw
437EE-3 Deadline: 16/6/2019 11:59PM HW 1 -4 sns4 is given; A signal x[n] 2 5 cos(n)5 sin(0.57n) Find and draw 1x[n 2. x[nJu[n 2] 3. x[n]. 8[n 21 4. -x[n2] 5. x[n(u[n-]-u[n-3]) 6. x[n+2] n+1 7. y[n] = 2k=n-1X[K] 8. x[n]8[-n-4 9 -x-n 2 10. x2n/2]
437EE-3 Deadline: 16/6/2019 11:59PM HW 1 -4 sns4 is given; A signal x[n] 2 5 cos(n)5 sin(0.57n) Find and draw 1x[n 2. x[nJu[n 2] 3. x[n]. 8[n 21 4. -x[n2] 5....
COMP Discrete Structures: Please answer completely and
clearly.
(3).
(5).
x) (4 points) If k is a positive integer, a k-coloring of a graph G is an assignment of one of k possible colors to each of the vertices/edges of G so that adjacent vertices/edges have different colors. Draw pictures of each of the following (a) A 4-coloring of the edges of the Petersen graph. (b) A 3-coloring of the vertices of the Petersen graph. (e) A 2-coloring (d) A...