# Area summation problem under a curve

1. Apr 8, 2017

### Karol

1. The problem statement, all variables and given/known data

Why, in:
$$\frac{\sqrt{1}+\sqrt{2}+...+\sqrt{n}}{n^{3/2}}$$
There is $~n^{3/2}$ in the denominator?

2. Relevant equations

3. The attempt at a solution
it should be:
$$S_n=\sqrt{c_1}\Delta x+\sqrt{c_2}\Delta x+...=\Delta x\cdot \sqrt{\Delta x}+\Delta x\cdot \sqrt{2\Delta x}+...=\sqrt{\Delta x}\cdot \Delta x(\sqrt{1}+\sqrt{2}+...+\sqrt{n})$$

2. Apr 8, 2017

### Staff: Mentor

It should be $\sum_k f(c_k) \Delta x$. Now $c_k=k \cdot \Delta x\, , \,f(c_k)=\sqrt{c_k}$ and $\Delta x=\frac{1}{n}$. You simply stopped too soon before substituting $\Delta x=\frac{1}{n}$.

3. Apr 9, 2017

### Karol

Thank you fresh_42