Integration using Riemann sums

**The question:**

Suppose that

i) Show that f is increasing on the interval [0, 1/2].

ii) Find the upper Riemann sum for f with respect to the partition

{ } of [0, 1/2]

iii) Hence evaluate limit n -> infinity ( )

**My attempt:**

i) I took the derivative of f, and found the stationary points by equating it to 0. I noticed that the only stationary point was at 0 itself, thus the graph may only change gradient at this point. I substituted for 1/2 and found that the gradient was positive, so the interval [0, 1/2] is increasing.

ii) I worked out the width of each partition is , and the height of a given partition 'k' is . My sum then looked something like this:

This looks different to what's in part iii). Is it incorrect? Also, how do I solve part iii)? Thanks.