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Recurrence relations

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

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Recurrence relations

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  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

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