Please show lots of detailed work. Thank you. Exercise 2.5. Use the Binomial Theorem to prove...
Please show your detailed work! Thank you! Prove the correctness of the following formulas using Induction: a. sigma_i=0^n i^3 = n^2(n + 1)^2/4 b. 1 + 2 + 4 + ... + 2^n = 2^(n+1) -1, for n greaterthanorequalto 0
Please show work/explain answer. Use the binomial theorem to expand (x + 2y)^5. You must illustrate use of the binomial theorem.
Prove the Binomial Theorem, that is Exercises 173 (vi) x+y y for all n e N C) Recall that for all 0rS L is divisible by 8 when n is an odd natural number vii))Show that 2 (vin) Prove Leibniz's Theorem for repeated differentiation of a product: If ande are functions of x, then prove that d (uv) d + +Mat0 for all n e N, where u, and d'a d/v and dy da respectively denote (You will need to...
please show all the work. if you use excel please show the screenshots. Thank you ! I Question 2 (20pts) Consider the following set of ordered pairs. Complete parts a through c. у Х 1 3 5 4 10 8 4 a) Calculate the slope and y-intercept for these data. (Round to four decimal places as needed.) b) Calculate the total sum of squares (SST). (Round to two decimal place as needed.) c) Partition the sum of squares into the...
prove e EOLU Exercise 4.1.1. Prove Theorem 4.1.6. (Hints: for (a) and (b), use the root test (Theorem 7.5.1). For (c), use the Weierstrass M-test (Theorem 3.5.7). For (d). use Theorem 3.7.1. For (e), use Corollary 3.6.2. The signale UI tre rauUS UI CUNvergence is the IUIUWII. Theorem 4.1.6. Let - Cn(x-a)" be a formal power series, and let R be its radius of convergence. (e) (Integration of power series) For any closed interval [y, z] con- tained in (a...
(complete the proof. Hint: Use the Squeeze Theorem to show that lima = L.) 3- For all ne N, let an = Let S = {a, neN). 3-1) Use the fact that lim 0 and the result of Exercise 1 to show that OES'. 3-2) Use the result of Exercise 2 to show that S - {0}. 4- Prove that
1. Use the binomial theorem to show i) Ek_0 () = 21; ii) _o(-1)* (m.) = 0; and finally that the sum of the ( over odd k equals that over the even k and that both are 21-1. (Hint: for iii) add and subtract the results of i) and ii). For i) and ii) put x and y equal to suitable values in the binomial theorem). (15 points)
please use Bayes theorem and show work. thank you :) PROBLEM 1 Assume that 0.5% of all semiconductor parts produced in a manufacturing process break within one year. The parts can be tested with a very reliable but not perfect screening procedure: • 2.5% of the parts that break within one year pass the test 1% of the parts that do not break within one year do not pass the test A part just failed this test. What is the...
Please show work and explain. Thank you. I rate correct work! Use either Stokes' theorem or the divergence theorem to evaluate each of the following integrals in the easiest possible way.
ANSWER 5,6 & 7 please. Show work for my understanding and upvote. THANK YOU!! Problem 5. (3 pts) Let {x,n} be a bounded sequence of real numbers and let E = {xn : n E N}. Prove that lim inf,,0 In and lim inf, Yn are both in E. Hint: Use the sequential characterization of the closure, i.e., Proposition 3.2 from class. Problem 6. (3 pts) As usual let Q denote the set of all rational numbers. Prove that R....