Hello,

Because at the end of each week he sells k chickens, there are weeks of selling (and rearing).

THE REARING

1st week :1000x0.5

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

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

.

.

.

th week :because so far, he has sold chickens.

th week :

So the total is :

Oh yeah, this is awful...

Factoring by 0.5, we get :

You can see that 1000 minus the red terms belong to an arithmetic sequence of general term : , starting at n=0, finishing at n= , and of progression -k

---> there are terms.

So :

This is the formula you should know. But we're starting at a_0, so it's different

, ,

--->

If something is unclear, tell me.. And if you think there is an easier way.. I'd agree with you