Find the limit by using Riemann integrals of suitably chosen function(s): $\displaystyle \lim_{n\to\infty} \left(\frac{2^\frac{1}{n}}{n+1}\right) + \left(\frac{2^\frac{2}{n}}{n+\left(\frac{1}{2}\right)}\right) +\dots + \left(\frac{2^\frac{n}{n}}{n+\left(\frac{1}{n}\right)}\right)$
I know that with Riemann sums it's best to find the limit summation $(\Delta x) (f(x_i))$. So I changed the question to look like a summation.
$$\left(\frac{1}{n}\right) \lim_{n\to\infty}\sum_{i=1}^{n} \left(\frac{2^{\left(\frac{i}{n}\right)}n}{n+ \left(\frac{1}{i}\right)}\right)$$
However, if I set the integral I am left with some ns in the denominator that I am not sure what to do with: $\displaystyle \int_{0}^{1} \left(\frac{2^xnx}{nx+1}\right) \,dx $
Am I even approaching this question in the right way? If so, what do I do with the $n$s? Any guidance would be helpful!