Question: Find $\lim_{n \to ∞}$ $(1+2^{0.5} + ..... n^{0.5})/n^{3/2}$
I have made this the sum from $\displaystyle \sum_{k=1}^n {k^{0.5}\over n^{3/2}}$ and want to make this a definite integral, however it is not of the form needed for this process normally. Do I let $\Delta x = 1/n^{3/4}$? Any help appreciated.
You can define the summation as following $$\displaystyle \sum_{k=1}^n {k^{0.5}\over n^{3/2}}={1\over n}\sum_{k=1}^n ({k\over n})^{0.5}$$and proceed by taking $f(x)=\sqrt x$.