How do you do part (c)? Is there a shorter way than calculating everything upto 100?
How do you do part (c)?
Is there a shorter way than calculating everything up to 100?
(c) Find the area of Figure 100.
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: