Insect Population Control T86921

Field biologists run a field experiment over $n$ days to assess the population of an invasor insect species.

An insect trap is set on the first day, and a new trap is added every day, so on the $i$th day, $i$ traps are deployed. Each trap is expected to capture $K$ individuals. However, specimens learn to avoid traps, so the effectiveness of the traps decays with time.

For this, the expected number of captured individuals on the $i$-th day is: $$E_i = \frac{K*i}{i!}$$ Thus, the accumulated number of captures after $n$ days of field work will be: $$C(n) = \sum_{i=1}^{n}\frac{K*i}{i!}$$

Write a function captures(n,K) that receives two integers: the number of days of the field experiment ($n$) and the expected captures per trap ($K$) and returns the expected accumulated number of captures $C(n)$ at the end of the field experiment.

Observation

• You are not allowed to import any function from math module.

• Using lists is not necessary, and will severely penalize your grade.

• Only the function is expected. If you have a main program to test it, comment it out, or put it inside an if __name__ == "__main__": conditional.