15, CAS Project. sec, tan. (a) Euler numbers. The defines the Bernoulli numbers B,n. Using undetermined Maclaurin series coefficients, show that E4 + 74 4! (23) Bi-1, B2 , B3-0, (21) sec z=E0--2,2 2! defines the Euler numbers E2n. Show that Eo 1, Write a program for computing Bn E21, E4 5, E6 -61. Write a program that (c)Tangent. Using (1), (2), Sec. 13.6, and (22), shorw computes the E2n from the coefficient formula in (I) or extracts them as a list from the series. (For tables calculate from it a table of BoB see Ref. [GenRefl], p. 810, listed in App. 1.) D) Bernoulli numbers. The Maclaurin series that tan z has the following Maclaurin series and 2i 4i (24) tan z= 4iz 2 22n(221) 2m- (22) n=1 15, CAS Project. sec, tan. (a) Euler numbers. The defines the Bernoulli numbers B,n. Using undetermined Maclaurin series coefficients, show that E4 + 74 4! (23) Bi-1, B2 , B3-0, (21) sec z=E0--2,2 2! defines the Euler numbers E2n. Show that Eo 1, Write a program for computing Bn E21, E4 5, E6 -61. Write a program that (c)Tangent. Using (1), (2), Sec. 13.6, and (22), shorw computes the E2n from the coefficient formula in (I) or extracts them as a list from the series. (For tables calculate from it a table of BoB see Ref. [GenRefl], p. 810, listed in App. 1.) D) Bernoulli numbers. The Maclaurin series that tan z has the following Maclaurin series and 2i 4i (24) tan z= 4iz 2 22n(221) 2m- (22) n=1