Let's look at the left sum first:

and so we have:

To compute the sum, I used an identity of Lagrange:

Now, to compute the limit:

We have the indeterminate form so applying L'Hôpital's rule, we find:

Now we have the indeterminate form , so applying L'Hôpital's rule again:

Now, see if you can do the same for the remaining two sums.