8.1: Recurrence Relations

• We touched on them briefly before; we’ll dive deeper here.

• We aren’t going to focus on solving them, but you should know how to prove a closed form is a solution from what we did before.

You start an account with $1000. At the end of each year, you add 5% of that year’s amount AND 3% of the previous year’s amount.Find An, the amount after n years.

How many bit strings of length n contain no consecutive 0s?

How many bit strings of length n contain no consecutive 0s?Let Sn be the set of bit strings of length n with no consecutive 0s. Find a recurrence relation for |Sn|

You can climb stairs 1 or two at a time. Find a RR for Wn, the number of ways you can climb a staircase with n stairs, when order matters.

Nicely written solution

Let n be a nonnegative integer. Let Rn denote the number of regions in a plane subdivided by n lines, with no two lines parallel and no three lines meeting in one point.