Originally Posted by

**Moo** Hello,

Because at the end of each week he sells k chickens, there are $\displaystyle \frac{1000}{k}$ weeks of selling (and rearing).

THE REARING

**1st week :** 1000x0.5

**2nd week :** (1000-k)x0.5

**3rd week :** (1000-2k)x0.5

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**$\displaystyle \left(\frac{1000}{k}-1\right)$ th week :** $\displaystyle \left(1000-\left(\frac{1000}{k}-1\right)k\right) \times 0.5$ because so far, he has sold $\displaystyle \left(\frac{1000}{k}-1\right)k$ chickens.

**$\displaystyle \frac{1000}{k}$ th week :** $\displaystyle \left(1000-\left(\frac{1000}{k}\right)k\right) \times 0.5=0$

So the total is :

$\displaystyle 1000 \times 0.5+(1000-k) \times 0.5+(1000-2k) \times 0.5+ \dots +$$\displaystyle \left(1000-\left(\frac{1000}{k}-1\right)k\right) \times 0.5$