Area of squares and rectangles

1
Area of squares and rectangles

• Consider the pattern of squares

2
Area of squares and rectangles

• Two ways of finding the area of the large
  rectangle

12 12 22 32 52 82 132 212 342

34 55

• Generalising, this gives the conjecture

3
Area of squares and rectangles

• Prove by induction

Show true for n 1
LHS
1
RHS
1
Hence true for n 1
4
Area of squares and rectangles

• Proof by induction

Assume true for n k
Show true for n k1
5
Area of squares and rectangles

• Proof by induction