1 / 10

Recurrence relations

Recurrence relations. It is an equation that relates the n -th term to certain of its predecessors. Compound Interest.

arlais
Télécharger la présentation

Recurrence relations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Recurrence relations It is an equation that relates the n-th term to certain of its predecessors.

  2. Compound Interest • A person invests $1000 at 12 % interest compounded annually. If a(n) represents the amount at the end of n years, find a recurrence relation and initial conditions that define the sequence a(n).

  3. Climbing Stairs • An elf has a staircase of n stairs to climb. Each step it takes can cover either 1 stair or 2 stairs. • Find a recurrence relation for the number of different ways for the elf to ascent the n-staircase.

  4. Dividing the Plane • Suppose we draw n straight lines on a piece of paper so that every pair of lines intersect, but no three lines intersect at a point. • Find a recurrence relation for the number of regions which these n lines divide the plane into.

  5. Fibonacci’s rabbit

  6. Recurrence relations

  7. Tower of Hanoi • There are 3 pegs mounted on a board and n disks of various sizes with holes in their centers. Initially the disks are stacked from the largest to the smallest on one peg. • The goal is to move the entire tower to another peg. The rule is • You can move only one disk at a time. • You can not place a larger disk on a smaller one.

  8. http://nlvm.usu.edu/en/nav/frames_asid_118_g_3_t_2.html

More Related