5. Given an integer n 2 1, define J(n) = 1+ 7 + ... + -. We want to extend the function J to other values than positive integers. The starting point is the equality 1+t+ t' t ... + en_ 1 -to+1 1 -t (a) (3 marks) Show that J(n) = 1_ ydt. Hint: Rewrite the integrand as a finite sum 1+t+ .... (b) (3 marks) Given a real number x 2 0, define gr(t) := It 1 - t . Show that lim gr(t) = x. t-+1- Given any x 2 0, part (b) shows that gr(t) extends to a continuous function of t on [0, 1], so that the function J(x) = 1 -t dt is defined on [0, co) and, by part (a), coincides with J(n) on positive integers. (c) (3 marks) Given any x