# Math Help - Evaluate function?

1. ## Evaluate function?

If $f(x) = \frac{a^x}{a^x + \sqrt{a}}\ (a > 0)$, evaluate $\sum_{r = 1}^{2n - 1} 2f\left(\frac{r}{2n}\right)$

2. Originally Posted by fardeen_gen
If $f(x) = \frac{a^x}{a^x + \sqrt{a}}\ (a > 0)$, evaluate $\sum_{r = 1}^{2n - 1} 2f\left(\frac{r}{2n}\right)$
And according to your previous post, this should be equal to (2n-1)

3. Originally Posted by fardeen_gen
If $f(x) = \frac{a^x}{a^x + \sqrt{a}}\ (a > 0)$, evaluate $\sum_{r = 1}^{2n - 1} 2f\left(\frac{r}{2n}\right)$
Write $f(x) = \frac1{1 + a^{\frac12 - x}}$

Observe that $f\left(\frac{r}{2n}\right) + f\left(\frac{2n - r}{2n}\right) = 1$

Thus grouping terms you get the sum to be $2n-1$ and not $1$.