(a) Evaluate

(b) A square grid of dots may be divided up into a set of L-shaped groups as illustrated in Figure 1.35.

How many dots are inside the third L shape?
How many extra dots are needed to extend the 3 by 3 square to one of side 4 by 4? How many dots are needed to extend an (r – 1) by (r – 1) square to one of size r by r? Denoting this number by P_r, use a geometric argument to obtain an expression for

and verify your conclusion by direct calculation in the case n =10.

3 n=-2 [n++3(-1)"]