Exercise

Approximate Pi with recursion

The number $\pi$ can be computed by the following formula: $$ \pi = 4\sum_{k=0}^{\infty}\frac{(-1)^k}{2k+1}=4\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\frac{1}{9}-…\right) $$ Your task is to write a recursive function to approximate $\pi$ using the formula defined above (the approximation means that instead of infinity $\infty$, the sequence considers only a certain amount of elements $n$).

Here are examples of $\pi$ for some of the values of $n$:
$n=0 \rightarrow \pi = 4$
$n=1 \rightarrow \pi \approx 2.67$
$n=2 \rightarrow \pi \approx 3.47$

Instructions 1/2

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Write a lambda expression calculating the $k$-th element in the series (without taking 4 into account).