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induction...
a population increases such that if there are N at the start of the week, there are a + bN at the end. 0 < b < 1.
show that at the end of c weeks the population is a((1-b^c)/(1-b)) + Nb^c
---
ok so it's induction.
show it works for 1... c = k...
c = k + 1
sum = b(a((1-b^k)/(1-b)) + Nb^k) + a
right? then it should turn out as a((1-b^(k+1))/(1-b)) + Nb^(k+1) when juggled about
but i can't rearrange it correctly. please help
show that at the end of c weeks the population is a((1-b^c)/(1-b)) + Nb^c
---
ok so it's induction.
show it works for 1... c = k...
c = k + 1
sum = b(a((1-b^k)/(1-b)) + Nb^k) + a
right? then it should turn out as a((1-b^(k+1))/(1-b)) + Nb^(k+1) when juggled about
but i can't rearrange it correctly. please help
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