Hello, fleurdel!
How do you do part (c)?
Is there a shorter way than calculating everything up to 100?
(c) Find the area of Figure 100.
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We have this sequence: .
Take the difference of consecutive terms,
. . then take the difference of the differences, and so on.
. .
We see that the second differences are constant.
This mean that the generating function is of the second degree . . . a quadratic.
The general quadratic function is:
Use the first three terms of the sequence to construct a system of equations:
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. .
. .
. .