If a,b are positive quantities and a₁=a+b/2,b₁=under root a₁b*a₂=a₁+b_1//2,b₂=under root a₂b₁ & so on lim n tends to infinity is equal to ?

ans is under root  b²-a² /cos ^-1 a/b   (q taken from tatamac graw hill comp aieee 2008-pg 26.26)

Pls see http://www.goiit.com/posts/list/trignometry-if-a-b-are-positive-quantities-and-if-41432.htm#209888