Using the Binomial Theorem, show that
Using the Binomial Theorem, show that 9. Using the Binomial Theorem, show that Σ
The binomial theorem states that (a + b)n = Σ (prbn_k. (a) Use the binomial theorem to show that 2k-0 W = 2n. (Hint, 2n= (1 + 1)n.) (b) Expand (a2 + b)4.
9. Using the Binomial Theorem, show that Σk㈡-n 2n-1
b) Using the binomial theorem show that Σ (-1)"/2 (n) cos" k(z) sink(z), Σ (-1)(k-1)/2C) cox"-"(x) sink(z). cos(nx) = sin(nx) = COS k-odd 6 marks]
Use the Binomial Theorem to show that Σ(-1): c(n, k)= 0 -0
5. Use the binomial theorem to show EX-.Q) = 2".
(d) Explain briefly the Central Limit Theorem. Using this theorem, how can you approximate the Binomial distribution?
39. Expand the expression (x + 3)5 using the Binomial Theorem.
Please show work/explain answer. Use the binomial theorem to expand (x + 2y)^5. You must illustrate use of the binomial theorem.
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)
7. Complete the proof of Theorem 1.2.2 (Replication in the N-period binomial model). Show under the induction hypothesis that