Please show work/explain answer. Use the binomial theorem to expand (x + 2y)^5. You must illustrate use of the binomial theorem.
show all steps please Use Binomial Series to expand the expression (1+x?)' into a polynomial.
Using the Binomial Theorem, show that 9. Using the Binomial Theorem, show that Σ
please hell with 13, 14, 15, 16, 17 13. Use the binomial theorem to expand: (w-11) 14. Use mathematical induction to prove the following: 3+ 7 + 11 + 15 + ... + (4n-1) = n(2n+1) 15. Write an expression for the n" term of the sequence 2! 3! 4! 5! 6! 7! 4'5'6'7'8'9' 16. The sixth term of an arithmetic sequence is 20.6, and the ninth term is 30.2. a. Find the nth term b. Find the 20 term...
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.
8. (15 points) Let X ~ Binomial(30,0.6). (a) (5 points) Using the Central Limit Theorem (CLT), approximate the probability that P(X > 20). (b) (5 points) Using CLT, approximate the probability that P(X = 18). (c) (5 points) Calculate P(X = 18) exactly and compare to part(b).
(1 point) The Binomial Theorem. Let p(x)=(2x−1)5=ax5+bx4+cx3+dx2+ex+f.p(x)=(2x−1)5=ax5+bx4+cx3+dx2+ex+f. Then (1 point) The Binomial Theorem. Let p(x) = (2x - 1)5 = ar” + bx4 + cr3 + de? + ex+f. Then , and
PLEASE DO BOTH (3) (5 pts) Find the expansion of (2x + y) using the binomial theorem? (4) (5 pts) What is the coefficient of z' in the expansion of (2 + x)?
Expand the following binomial. (2x+3)4
Use the binomial series to expand the function as a power series. f (x) = 5/1+ -5/1+ 6 15(-1)*+1 (0) 2n! IM n=0 00 5 5+ 12+ + [51-1)^-1 (a)" 2n! n=2 72 5+ =1041.32... (2n – 1) () 72 5+ 5(-1)"1.3.5. .... (2n - 3) 2n! n=2 (2n – 3) 72 5 5+ - + 12" 5(-1)n-11.3.5.... 2n! n=2 State the radius of convergence, R. (If the radius of convergence is infinity, enter INFINITY.) R = X Need Heln2...