Does anyone can post a full solution of each parts? thanks a lot

2. Let ST. = = [1 + 21/m + 23/m + ...+ 2(0-1)/m]. (a) (5 points) Find lim S,, without using any knowledge of Riemann integral. (b) (3 points) Determine a function f(r) and sample points {z;), such that Sn is a Riemann sum of f(x) on [0, 1]. (c) (2 points) Find lim S 4 Sa by any method, where S.. = [21/m + 2(1+1/V2)/m+ 2(2+1/v3)/"+...+ 2(0-1+1/v0)/0]