Transcript Fibonacci’s Numbers

It is an equation that relates the n-th term to
certain of its predecessors.

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).
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
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 nstaircase.
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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.
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1.
2.
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.
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