Limits of sums by computer

You will test three limits of sums on the computer. The first function adds the right-hand terms for any $f$. The other two use it on the sums of the lesson.

The idea. The sum $\dfrac{1}{n}\displaystyle\sum_{r=1}^{n}f\left(\dfrac{r}{n}\right)$ tends to $\displaystyle\int_0^1 f(x)\,dx$. A sum such as $\displaystyle\sum_{r=1}^{n}\dfrac{1}{n + r}$ is of this form with $f(x) = \dfrac{1}{1 + x}$. A product is turned into a sum with a logarithm, and then back with an exponential.

Your tasks.

1. Finish riemann(f, n). Return $\dfrac{1}{n}\displaystyle\sum_{r=1}^{n}f\left(\dfrac{r}{n}\right)$.
2. Finish harmonic_block(n). Return $\displaystyle\sum_{r=1}^{n}\dfrac{1}{n + r}$.
3. Finish product_limit(n). Return $\dfrac{1}{n}\Bigl[(n + 1)(n + 2)\cdots(2n)\Bigr]^{1/n}$, found as exp of the average of log(1 + r / n).