Q11 (Variant of Wallis product). For every integer n 2 0, we define Im r sin dx (a) Show that In+...

Question

Question

Q11 (Variant of Wallis product). For every integer n 2 0, we define Im r sin dx (a) Show that In+,-n+21n (b) Show that 0< 12n

Answer 1

Answer #1

2.44 LHS Sinue ん 2n-1 2n+l a n n+卡 ^ 나 11+1 千 ve have nt2 互n+ nの 22m Sin

Answer 2

Similar Homework Help Questions

Q9 (Approximation of π) (a) Show that 1/1 + t2 = 1 − t2 + t4 − ... + (−1)n−1 t 2n−2 + (−1)n t2n /1 + t2 for all t ∈ R and n ∈ N. (b) Integrate both side in (a), show that tan−1 (x) = x − x3/3 + x5 /5...

Q9 (Approximation of π) (a) Show that 1/1 + t2 = 1 − t2 + t4 − ... + (−1)n−1 t 2n−2 + (−1)n t2n /1 + t2 for all t ∈ R and n ∈ N. (b) Integrate both side in (a), show that tan−1 (x) = x − x3/3 + x5 /5 − ... + (−1)n−1x 2n−1/ 2n − 1 + Z x 0 (−1)n t2n /1 + t2 dt. (c) Show that tan−1 (x) − ( x...
Ok = (6) Let n be a positive integer. For every integer k, define the 2...

Ok = (6) Let n be a positive integer. For every integer k, define the 2 x 2 matrix cos(27k/n) - sin(2nk/n) sin(2tk/n) cos(27 k/n) (a) Prove that go = I, that ok + oe for 0 < k < l< n - 1, and that Ok = Okun for all integers k. (b) Let o = 01. Prove that ok ok for all integers k. (c) Prove that {1,0,0%,...,ON-1} is a finite abelian group of order n.
Someone can help? For each n = 1,2,3,..., define fn (2):= (1 – 22n), for every...

Someone can help? For each n = 1,2,3,..., define fn (2):= (1 – 22n), for every € (-1,1]. Then the function fdefined by f(2):= lim fn (2) exists for each x € (-1,1) and is equal to 1200 Select one: Of(x) = 0 Of(x) = 2 f(2)= so 2 <1 1 2 = 1 Of(2) { Sx |x|<1 0.2 = 1 28y = 0 Dy2 Consider the following partial differential equation (PDE): ori or where u= u(x, y) is the...