A sequence is defined by the first-order recurrence relation: an=5an-1+3 a0=4 a) Write out the first 5 terms of this sequence. b) Given that: an=A*5n+B Show that A=19/4 and B=-3/4. c) Use mathematical induction to prove that ?n = 19/4 × 5n – 3/4
HW Help? I cannot seem to figure this one out.. --Write a program that reads the integers between 1 and 100 and counts the occurrences of each. assume the input ends with 0. Example: 2 5 6 5 4 3 23 43 2 0 ENTER 2 occurs 2 times 3 occurs 1 time 4 occurs 1 time 5 occurs 2 times 6 occurs 1 time 23 occurs 1 time 43 occurs 1 time Note that if a number occurs more...
Problem 9 Consider the directed network on vertices V s, 1,2,3, 4,5,t) given by the following list. An element of this list has the forn (í,j,c) where (i,j) is an are of the network, and c is the capacity of are (i.j) (3, 4,2), (3,,15), (3, 5,11), (3, t, 12, (4,5,9), (4, t, 15), (5,t,7) ·What is the maximuln 8 → t flow in this network? (You may use AMPL to compute this.) What is a minimum cut? EXTRA CREDIT;...
2- 4. Given the Sequence below(-3)***** a) Write the first five terms of the sequence. b) Provide a sketch for the first five terms of the sequence. Does the sequence approach a number? c) Does the sequence Converge or Diverge as no? Explain your answer. d) Find lim,--..(am + b), where a, the general term you found in a) and m2+1 Does the limit converge?
(1 point) Write out the first five terms of the sequence a n = (-1)^ n-1 (n+4)^ 2 Enter the following information for a, a 1 = a 2 = a 3 = a 4 = a 5 = lim n infty (-1)^ n-1 (n+4)^ 2 = Box (Enter DNE if limit Does Not Exist.) Does the sequence converge Bigg[ (-1)^ n-1 (n+4)^ 2 Bigg] n=1 ^ infty determine whether the sequence converges, and if so find its limit. (Enter...
5. Use Newton's Binomial Theorem to write y- V1- 2 as an infinite series (write out at least four non-zero terms) and apply Rule I of De analysi term-by-term to find the area under the curve y-V1-x2 in the first quadrant (again using at least four non-zero terms). Using only the first four non-zero terms in the series you found, estimate the value of T. (Remark: This is a very inefficient way to estimate π. Using 1000 terms of the...
8. Build a power series by long division. a) Write out first 4 terms. b) Write result in summation notation. f(x)= 2-2x 143
I need help with number 3 on my number theory hw. Exercise 1. Figure out how many solutions x2 = x (mod n) has for n = 5,6,7, and then compute how many solutions there are modulo 210. Exercise 2. (a) Find all solutions to x2 +8 = 0 (mod 11). (b) Using your answer to part (a) and Hensel's Lemma, find all solutions to x2 +8 = 0 (mod 121). Exercise 3. Solve f(x) = x3 – x2 +...
(2) Prove that if j-0 i-0 with k, 1 e N u {0), and bo, . . . , be , do, . . . , dl e { 0, . . . , 9), such that be, de # 0, then k = 1 and bi- di fori 0,.. , k. (I recommend using strong induction and uniqueness of the expression n=10 . a + r with a e Z and re(0, 1, ,9).) (3) Prove that for all...
In this exercise we consider finding the first five coefficients in the series solution of the first order linear initial value problem (+3)y' 2y 0 subject to the initial condition y(0) 1. Since the equation has an ordinary point at z 0 it has a power series solution in the form We learned how to easily solve problems like this separation of variables but here we want to consider the power series method (1) Insert the formal power series into...